We cannot but fail to be in awe of Montresor, his criminal cunning and his psychological understanding of his enemy as he seems to know exactly what words to say and how to tempt Fortunato down into his catacombs and ever closer to his fate. We are not told who specifically Luchesi is, but we can infer that he is another nobleman, like Montresor and Fortunato, but one who has experience with wines and spirits, as Montresor says that he will go to Luchesi to verify if the drink he has obtained is Amontillado or not:
"As you are engaged, I am on my way to Luchesi. If anyone has a critical turn, it is he. He will tell me--"
Montresor knows what pride Fortunato takes in his knowledge of vintage Italian wines and how important this is to him. By subtley suggesting that Luchesi has more knowledge and skill in this area, by refering to his "critical turn," he is challenging Fortunato's sense of pride and his skill, thus ensuring that Fortunato, for his honour and pride, will follow him. Luchesi, then, is a character that we never meet, but whose purpose is to function as bait that Montresor calculatingly uses to reel Fortunato in to his trap.
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.