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.
I do not believe that Poe intended that his character Fortunato would actually want to give Montresor an honest opinion of the nonexistent Amontillado. I believe that Montresor was supposed to know in advance that if he told Fortunato he had bought a whole pipe of Amontillado at a "bargain" price, Fortunato would be mostly interested in getting in on this bargain himself. He would plan from the beginning to tell Montresor that the wine was not genuine but only ordinary Sherry--regardless of whether this was true or false. If the nonexistent wine had turned out to be ordinary Sherry, Fortunato would only be telling the plain truth. If it was genuine Amontillado, he would still declare it to be ordinary Sherry so as to eliminate Montresor as a buyer for more--and also to prevent Montresor from saying anything about it to the competitor named Luchesi. Montresor knows Fortunato's character. He has suffered similar "injuries" from him in business deals in the past. Fortunato, for his part, would consider it an "excellent jest" to cheat both Montresor and Luchesi out of an opportunity to buy genuine Amontillado at a bargain price.
Fortunato is not, in my opinion, interesting in helping a friend, or in displaying his "virtuosity" as a connoisseur of wines, or in drinking a glass of Amontillado in a dank catacomb full of human bones when he is inadequately dressed for such an excursion and has a bad cold. He is interested in the "bargain." He is a rich man. He could make a small fortune buying up a whole shipload of Amontillado in oak casks, bottling it, and selling it off at his leisure at a 100% markup. That type of wine only improves with age. So time was not an important factor in his calculations. In fact, Amontillado is highly regarded by gourmets just because it is aged.
Fortunato could not be interested both in displaying his connoisseurship and in declaring the wine to be ordinary Sherry if it is genuine Amontillado. It has to be one or the other. Montresor does not believe he can lure Fortunato into his catacombs just by appealing to his egotism. In threatening to go to Luchesi, he is actually threatening to let another man, presumably a business rival, in on the secret that a Spanish ship is selling off a shipload of Amontillado at a bargain price. This fact has supposedly escaped notice by Fortunato and Luchesi because of "the supreme madness of the carnival season."
If Montresor has already bought and paid for the cask of wine and has had it transported to his vaults, then what is the big hurry about getting an opinion about its quality. Why is he rushing around at night looking for Fortunato and then planning to rush off to Luchesi? It can only be because he wants to buy more! He would have bought more in the first place, but, as he keeps says, he has his doubts about the genuineness of the wine. If he were only sure it was high-quality Amontillado, he would immediately buy as many casks as he could afford. He wants to find out immediately whether or not the wine is true Amontillado. Once its arrival in Venice becomes common knowledge, because of the action of the law of supply and demand, it will no longer be available at a bargain price.
Because Montresor recognizes that one of Fortunato's faults is his arrogance--he is proud of family, his position in society, his money, his expertise--Montresor uses this arrogance as the "bait" to get Fortunato to follow him into the catacombs to determine whether the Amontillado is genuine:
' As you are engaged, I am on my way to Luchesi. If any one has a critical eye, it is he. [Fortunato's immediate and arrogant reply] is, 'Luchesi cannot tell Amontillado from Sherry.'
Of all the possible motivations to get Fortunato to go on this journey, Montresor knows that Fortunato's arrogance is the only fool-proof way to commit Fortunato to this journey. Fortunato cannot stand the thought that someone else might have more skill than he does.
Later, in the catacombs when Fortunato has a coughing fit, Montresor suggests that they go back, but he hooks Fortunato again by saying
'We will go back; you will be ill, and I cannot be responsible. Besides there is Luchesi---'
As in the beginning, Montresor plays on Fortunato's arrogance to get him to continue on this journey, which is obviously detrimental to his health. The last reference to Luchesi is designed to remind Fortunato that his knowledge of wine might easily replaced by Luchesi's skill, and that possibility is something Fortunato cannot allow.
Montresor, throughout the story, implies that Fortunato has done something horrible to Montresor. It is important, then, that we see Fortunato as excessive in every respect--including his arrogance.
In "The Cask of Amontillado" Luchresi serves as a kind of mechanism utilized by Montresor to coax Fortunato into the catacombs. Luchresi is mentioned only twice in the the story, but both are a moments where Fortunato makes decisions that allow Montresor to seal him in the vaults.
In the beginning of the story, Luchresi is introduced as Fortunato's rival:
"'As you are engaged, I am on my way to Luchresi. If any one has a critical turn it is he. He will tell me --'"
"'Luchresi cannot tell Amontillado from Sherry.'"
It is this wine tasting rivalry that motivates Fortunato to follow Montresor and find the Amontillado. He believes himself far more competent than Luchresi and intends to prove himself as such.
The second instance is Luchresi is mentioned is right before Montesor leaves Fortunato to dies in the vaults. Montesor mentions Luchresi to distract, confuse, and anger Fortunado. Furthermore, Fortunado reiterates his superiority and most likely gains a false sense of security. This allows Montesor to catch him off guard.
"Proceed," I said; "herein is the Amontillado. As for Luchresi --"
"He is an ignoramus," interrupted my friend, as he stepped unsteadily forward, while I followed immediately at his heels. In niche, and finding an instant he had reached the extremity of the niche, and finding his progress arrested by the rock, stood stupidly bewildered.