As they head to catacombs, Fortunato states, “I will die of a cough.“ What is ironic about this statement?

After Montresor successfully manipulates Fortunato into following him down into the depths of his family's catacombs—ostensibly to try the expensive, rare Amontillado wine—Fortunato begins to cough severely in the vaults. Montresor pretends to worry about Fortunato's health and insists that they turn around. Fortunato responds by saying, "Enough . . . the cough's a mere nothing; it will not kill me. I shall not die of a cough." In a brilliant use of irony, Montresor replies, "True —true."
Irony is a figure of speech in which words are used in such a way that their intended meaning is different from the actual meaning. Montresor's words are also an example of dramatic irony, which is when the audience knows something that the characters do not. The audience is aware that Montresor will murder Fortunato and knows that Fortunato will "not die of a cough" (because he's going to be killed by Montresor instead). While Montresor's words appear to be genuine and to show concern for Fortunato's health, he is actually confirming that Fortunato will die a different way. Later on, Montresor shackles Fortunato to the back wall of the vaults and buries him alive by building a wall around him.
https://literarydevices.net/verbal-irony/

Fortunato actually says he will not die of a cough. When he starts coughing because of the nitre on the walls of the catacombs, Montresor suggests they go back to upstairs to spare his health. He says he will let Fortunato's rival, Luchesi, taste the amontillado instead. Fortunato replies as follows:

“Enough,” he said; “the cough is a mere nothing; it will not kill me. I shall not die of a cough.”

Montresor replies: "True—true."
Verbal irony occurs when a statement means the opposite of what it is intended to mean. What Fortunato means is that he knows he is healthy enough to expect to live a long life. In that sense, a few coughs are not going to kill him. But what that statement really means in the context of the story—and what Montresor means by saying "—is that a cough will not kill Fortunato because Montresor will kill him. His death will be due to being walled up alive in the catacombs by Montresor.