Discuss the obvious IRONY in this story: what is the role of luck or fortune.

There are many examples of irony in this story, many of them verbal (that is, instances where what is said is the opposite of what is really meant). Given the phrasing of your question, however, I think the "obvious irony" you refer to is grounded in Poe's naming conventions. The unfortunate Fortunato, whose name means fortune or luck, proves to be very unlucky indeed.
Fortunato is a clever and accomplished man. It is his one flaw or "weak point"—his pride in his knowledge of wine—which allows him to be brought low and his fortunes, so to speak, reversed. References to luck and fortune occur upon Fortunato's first appearance to ironic effect. Montresor says that Fortunato is "luckily met," when he knows that of course this will not be a lucky day for Fortunato at all. As the story goes on, Montresor offers Fortunato chances to go back and escape, but Fortunato is so fixated on the Amontillado that he does not take these chances. To a certain extent, we can say that he makes his own luck.
When Montresor first meets Fortunato in the story, he is wearing "motley," or a jester's outfit; this connotes that he is having a good time, but it is also the outfit of a court fool. While Fortunato is not, in general terms, a fool, his wearing of this cheery and comical outfit is ironic because on this occasion, Montresor is certainly able to make a fool of him. The ludicrous outfit makes reappearances as the story grows darker—the bells on the hat jingling with ironic cheer as Fortunato is led to his doom. At the very end of the story, after Montresor has thrust the torch into the aperture with the walled-in Fortunato, he hears only a faint jiingling of the bells, a last jest.