Fortunato, is not a man to be taken lightly, even in the inebriated state in which Montresor finds him. He also knows, however, that Fortunato is a man of considerable ego and that the best way of enticing Fortunato into his trap is by appealing to his vanity. By suggesting that he, Montresor, will ask this unseen character, Luchesi, about the cask of wine rather than asking Fortunato, he knows that the latter will rise to the bait. This is strongly hinted at in the following passage from early in Poe's story:

“As you are engaged, I am on my way to Luchesi. If any one has a critical turn, it is he. He will tell me——”

“Luchesi cannot tell Amontillado from Sherry.”

This one reference to Luchesi by Montresor does the trick. Fortunato takes the bait, but Montresor must continue to dangle the name of Luchesi before his victim to ensure Fortunato remains on track to enter the dungeon that awaits. That is why, Fortunato having entered the cellar of Montresor's home only to experience a respiratory episode caused by the foul mold-infected air in the basement, seems on the verge of turning around the leaving the home, thereby upsetting Montresor's plan to murder him. In order to prevent any such occurrence, Montresor again plays the "Luchesi" card: 

"You are rich, respected, admired, beloved;  you are happy, as once I was. You are a man to be missed. For me it is no matter. We will go back; you will be ill, and I cannot be responsible. Besides, there is Luchesi——”

The continued references to Luchesi are employed to ensure that Fortunato remains sufficiently intrigued and vain so as to continue along the path to his doom. Luchesi is never seen, but his presence is certainly felt.

I'm sure the person's name is Luchesi. Somehow it got spelled Luchresi in a few editions of the story, but most critics refer to him as Luchesi. This character never appears but is referred to by Montresor several times throughout the story. He is a wine connoisseur. When Montresor first encounters Fortunato in the street he tells him he needs someone to advise him whether the cask of wine he just bought is genuine Amontillado and says:

"Since you are engaged, I am on my way to Luchesi. If any one has a critical turn, it is he. He will tell me"--

This bit of dialogue has a dual purpose. Montresor is fishing: he wants to find out if Fortunato is expected anywhere that evening. If so, he would probably decide not to commit the murder on that occasion. He would like to leave a cold trail. He would prefer to have at least that night and the following day elapse before anyone missed his intended victim. He doesn't get the information he wants immediately. But when he repeats that he will consult Luchesi, Fortunato says:

"I have no engagement; come."

I have suggested elsewhere that all three men are "gentlemen-brokers" who survive in the declining city of Venice through buying and selling expensive things such as paintings, statues, gemmary (i.e. jewelry), and probably gourmet wines. The "pipe" of Amontillado Montresor claims to have bought would contain 126 gallons of wine. Fortunato is greatly interested because he would like to buy some himself--but he has to be sure it is genuine Amontillado. He knows that Luchesi would also be keen on buying some if he heard about it, and then he would be competing with Fortunato in bargaining with the seller. Montresor's apparently naive, innocent intention of consulting Luchesi motivates Fortunato to go to Montresor's palazzo that every night. Both Fortunato and Luchesi could probably afford to buy the entire shipment of Amontillado, whereas Montresor is a poor man and could probably only afford another two or three casks if he were assured by an expert that it was genuine.

Although Fortunato repeatedly disparages Luchesi's connoisseurship, he is deliberately lying in the hope of dissuading Montresor from consulting the other man. Fortunato is not eager to taste the nonexistent Amontillado because he is such a great wine-lover, or because he wishes to accommodate a friend, or because he wants to show of his expertise: he is hoping to make a lot of money by buying  many casks of gourmet wine and reselling it in quart bottles at a big profit. The good thing about wine as merchandise is that it improves with age if it is kept in wooden casks, so Fortunato (or Luchesi) could take their own sweet time about disposing of the Amontillado (if it really existed).

Finally, it is important to note that Fortunato would not have to go to Montresor's palazzo to taste the wine. Once he knows it is available for sale, he would have no trouble finding the ship that brought it into Venice. But if he makes some excuse (such as his cold) for not going that night, Montresor will go straight to Luchesi--and that is what Fortunato wants to forestall.

Poe needed something to lure Fortunato underground where Montresor could chain him to the rock wall and leave him to die. Wine was the best lure because Fortunato loved wine and was already drunk when Montresor found him in the street. But what kind of wine? It obviously couldn't be Italian wine because there was an abundance of that at all times, and especially during the "supreme madness" of the carnival. Montresor couldn't say that it was French wine because he was French himself and was a connoisseur of wine. He twice offers Fortunato French wines when they are down in the catacombs: Medoc and De Grave. The only other alternative was a Spanish wine. The Spanish export a lot of sherry, and the finest sherry is Amontillado. Poe may have known very little about Amontillado sherry, but he only needed to know a little for story purposes. The Amontillado, of course, never really existed.

Montresor uses Luchesi as a kind of spur to get Fortunato to come to Montresor's house to see the supposed Amontillado he's purchased.  Montresor has identified pride as Fortunato's weakness, and he calls up that pride in a couple of ways.  First, he tells Fortunato that he purchased a large quantity of Amontillado, a rare kind of Spanish wine, because he seems to know that Fortunato will not believe it.  Moreover, he knows that Fortunato will not want to pass up an opportunity to prove him wrong.  Even before they return to Montresor's home, Fortunato says, "'Amontillado?  A pipe?  Impossible!  And in the middle of the carnival!'" 

Second, Montresor knows that if he says he'll get another local wine connoisseur to verify the wine, this will further compel Fortunato because he will not want to believe that this other expert is as discerning and capable as he.  When Montresor says that he'll find Luchesi since Fortunato is obviously busy, Fortunato says, "'Amontillado!  You have been imposed upon.  And as for Luchesi, he cannot distinguish Sherry from Amontillado.'"  Fortunato believes that his expertise is superior to Luchesi's as well as Montresor's and he will not pass up this opportunity to exercise it, just as Montresor planned.

In terms of Montresor's other preparations, he's brought with him a "mask of black silk" as well as a "roquelaire" (or cloak) that he draws around himself.  This way, he cannot be identified by anyone who happens to see him and Fortunato together.  He also hides the trowel, a small spade one would use to lay brick, beneath his cloak.  Moreover, he was sure to tell his servants that he would "not return until the morning, and had given them explicit orders not to stir from the house," knowing full well that this would "insure their immediate disappearance, one and all, as soon as [his] back was turned."  Therefore, no one from Montresor's own household would be able to say that saw Montresor with Fortunato either.

The man called Luchesi (Luchresi in some editions) has no role in the story. Montresor has concocted an intricate falsehood to lure Fortunato down into the catacombs below his palazzo. The only thing that could get Fortunato to follow him underground would be a rare wine. So Montresor tells Fortunato the following:

"My dear Fortunato, you are luckily met. How remarkably well you are looking to-day! But I have received a pipe of Amontillado, and I have my doubts....You were not to be found, and I was fearful of losing a bargain."

Montresor wants to ascertain whether Fortunato is expected anywhere that night, because he wants to leave a cold trail. So he says:

"As you are engaged, I am on my way to Luchesi. If any one has a critical turn, it is he. He will tell me."

This is one of Montresor many lies. He has no intention of going to Luchesi, obviously another connoisseur, but he wants to force Fortunato to accompany him to his palazzo that night. Fortunato is keenly interested in the Amontillado, but he doesn't have to taste a sample from Montresor's "pipe" (126 gallons!!!). The wine must have come in by ship, and he could easily find the ship and taste the wine aboard it.

By pretending to be in such a big hurry, Montresor gives the impression that he would buy more if he were sure it is genuine. He pretends he has to act quickly. The wine, of course, does not exist--which is why he could not go to Luchesi. Neither Montresor nor Fortunato is interested in buying the wine for private consumption. If there is a bargain to be had, they can buy a large quantity and sell it off in bottles at a profit. But Fortunato knows if he refuses to go with Montresor, then Luchesi will find out about it, and he will be competing with him, both bidding up the price.

The ruse is very complicated. Montresor cannot simply ask Fortunato to come to his home and sample some wine that night--and he knows it. He mentions Luchesi in order to make Fortunato fear having a third party find out about the availability of a shipment of Amontillado at a bargain price. Fortunato, as Montresor is well aware, is thinking of finding the Spanish ship and buying up the entire cargo. Montresor is a poor man and probably could only afford a few of the big 126-gallon pipes himself.

Luchesi, on the other hand, might be able to buy in quantity. What Fortunato fears is that Luchesi would go with Montresor, taste the wine, then try to buy up the entire cargo himself--assuming that it is genuine. Of course, Montresor is lying about going to Luchesi. This potential competitor Luchesi never appears in the story.

Montresor finally gets the information he wants when Fortunato says:

"I have no engagement; come."

Later when Fortunato finds himself chained to the rock wall, he will pretend that he did have an "engagement"--that he is expected at home and will be missed that night. He is trying to scare Montresor into setting him free and pretending the whole thing is "an excellent jest" in order to give Montresor an alibi, an excuse for releasing him.

"But is it not getting late? Will not they be awaiting us at the palazzo, the Lady Fortunato and the rest? Let us be gone."

But the cunning Montresor has already found out that Fortunato is not expected at home or anywhere else. His victim's disappearance will not be noted until tomorrow at the earliest. By then no one will remember seeing Fortunato or a shadowy figure beside him dressed all in black and wearing a black mask.

The existence of Luchesi enables Montresor to lure Fortunato into his vaults more easily than saying he just needs Fortunato's advice. Luchesi is a way for Montresor to appeal to Fortunato's pride. Fortunato considers himself an expert in fine wine and his pride is hurt when Montresor says he will consult Luchesi. Montresor knows that one of Fortunato's main faults is pride and he therefore uses this trait against Fortunanto by constantly mentioning a possible rival to Fortunato's skills.

Montresor interests Fortunato in the nonexistent Amontillado by telling him that he bought it at a "bargain" price. Fortunato does not have to sample Montresor's Amontillado to make sure it is genuine before buying some of it, or all of it, himself. The wine must have arrived very recently aboard a ship from Barcelona. People, including dealers, haven't heard about it yet because it is "the supreme madness of the carnival," and everybody is neglecting ordinary business, including Fortunato himself. That is why it is, supposedly, a bargain. Fortunato could easily find that ship on the waterfront and taste the wine on board. Montresor knows this. Therefore he tells Fortunato he is on his way to find this Luchesi. Montresor appears anxious to get an opinion on his nonexistent Amontillado immediately. This can only be because it is now available at a bargain price, but it won't remain a bargain once word gets around that it has arrived in port. Fortunato does not want Luchesi to hear about the wine or the bargain price, so he is forced to accompany Montresor to his palazzo in spite of his bad cold and in spite of being inadequately dressed for the cold, dank catacombs. He disparages Luchesi as a wine connoisseur because he wants Montresor to depend on himself as judge. Montresor knows Fortunato from experience and understands that his friendly enemy is already planning to taste the (nonexistent) wine and declare it to be ordinary Sherry. Even before they leave the street he prepares Montresor for disappointment by saying, "You have been imposed upon." This will not only eliminate Luchesi as a possible competitor, but it will eliminate Montresor too. Montresor would not have pretended to be in such a hurry to get an opinion on his purchase if he didn't want to make Fortunato think he intended to buy more. He has already bought and paid for his pipe of Amontillado and had it moved to his palazzo--so why should he be so anxious to verify its quality now? Only because he would buy more if he were sure it was genuine.

Luchesi is important to the story! That was the major impetus Montressor used to lure Fortunato into the scheme. Luchesi was used as an affront to Fortunato's pride "And yet some fools would consider him as knowledgable as you." From that moment Fortunato was hooked as he could not back down from that challenge.

Luchresi never enters the story in the form of a character.  He is simply someone whose name is used in order to get Fortunato's interest up enough to encourage him to jump at the chance to try the amontillado.  Luchresi, like Fortunato, is another wine expert.  Montresor threatens to take Luchresi to the coveted amontillado if Fortunato isn't interested.

I have previously suggested that both Montresor and Fortunato are aristocrats but earn their livings by dealing in expensive goods such as paintings, antiques, jewelry (gemmary), and probably gourmet wines. This is implied in the third paragraph of the story which includes these sentences:

Few Italians have the true virtuoso spirit. For the most part their enthusiasm is adopted to suit the time and opportunity to practice imposture upon the British and Austrian millionaires. In painting and gemmary, Fortunato, like his countrymen, was a quack, but in the matter of old wines he was sincere.

When Montresor tells Fortunato that he has purchased a cask of Amontillado at a bargain price, Fortunato is naturally interested in buying some for himself. That is the main reason he wants to sample it. Montresor repeats that he has doubts about its genuineness. Obviously a ship carrying a whole cargo of the wine has recently arrived in Venice. Fortunato normally would have heard about it, but this is the height of the carnival and people have been neglecting business.

Fortunato would not need to sample Montresor’s wine. He could say he was too busy and would do it later. He would have no trouble finding a newly arrived Spanish ship loaded with big pipes of wine (each containing 126 gallons). That is why Montresor tells him

“As you are engaged, I am on my way to Luchesi.”

This is very good! He says, “I am on my way.” Time is of the essence. Luchesi must be another man who deals in luxury goods, another competitor. Fortunato does not want him to hear a word about the Amontillado. He accompanies Montresor to his vaults—not out of friendship or to show off his knowledge of wines, and certainly not to drink a glass of wine in a dank catacomb when he has a cold and is inadequately clothed--but in order to keep him from going to Luchesi. If Luchesi knew about the shipload of wine, he would find it quickly enough. Everybody on the waterfront would know about a newly arrived Spanish ship. Then Fortunato would have to be competing with the other aristocrat-connoisseur-businessman in bidding on the cargo. Both of them could sample the Amontillado (if it existed) aboard the ship to make sure it is genuine. There would be no need for either of them to taste Montresor’s wine.

Fortunato can afford to buy the whole shipload. Luchesi is probably able to do the same. Poor Montresor would be left with his one cask of Amontillado for whatever small profit he could make selling it in bottles. But Montresor knows Fortunato’s mind. Fortunato is already planning to taste the wine and tell him it is only ordinary sherry. Then, assuming it was genuine, Fortunato would go to find the captain of the Spanish ship. We can assume that tricks like these are among the “thousand injuries” Montresor has suffered over the years.

Why does he maintain relations with Fortunato? Fortunato is rich. Montresor may need to borrow money from him or to go into joint ventures with him if it is a question of buying an expensive item, such as an oil painting, for resale.