I would point out, as I think JMS did too, that we hear the prophecy spoken but do not see it written. Therefore the "eye" that does not see could very well be the "I" that does not see. As for the first two, one would assume that it had something to do with the either his first deal with Morden, or the one he made during "Coming of Shadows".
(Also, let me know if I should hide any of this below a spoiler cut, but I think since this is a spoiler thread I should be able to get away with it.)
It's a very tricksy prophecy. When I first heard it I thought she was saying that the first two options were already past, and therefore he had already failed with the "eye/I" and the killing. I guess we'll never know what they really were, but assuming then that all 3 avoidance points are in the future:
1) "The eye that does not see." In my opinion it can either be the "I" that does not see, just to cryptic, or we can assume a literal eye. If it had been a past event I would have assumed he needed to save the Imperial eye that Lord Kiro was after in "Signs and Portents" without Morden's help. Since its a future event, I think we have to assume it's G'Kar's eye (which "sees better" now that he has lost it). For some reason, if he had stuck around long enough to tell Cartagia to leave G'Kar alone, events might have somehow snowballed enough to save him from what comes later. (On a humorous note, maybe its the eye that G'Kar put in Sheridan and Delenn's wedding suite, and by helping him get it Londo does save himself!)
2) "You must not kill the one who is already dead." I think in this case it is referring to Morden. As epic as it was to see Morden get what was coming to him, and to see Vir's request to fulfilled, the event further doomed Londo. I would assume this is because as a result of Morden execution, the Drakh chose Centauri Prime as their base. Keep in mind, that had the Shadows been allowed to remain on Centauri Prime, they would have left with the Vorlons thus sparing the planet. Therefore, blowing up the island was unnecessary. Had it not been done, the Drakh would have remembered the Centauri as allies and not needed to punish them.
It's also possible that the very act of fulfilling Vir's wish also had an impact. I have a personal theory that Morden didn't "choose" Londo, rather Morden fulfills every request he is given, including the one he made with G'Kar (you'll note that G'Kar never sees Morden again, even in passing, and there are points where the Shadows could kill G'Kar but don't. I believe this is because they have a contract with him.) Perhaps by fulfilling the Shadow's contract with Vir to see Morden beheaded, Londo further doomed himself?
3) "You must sacrifice yourself." This could be one of two things - 1) accepting the Keeper or 2) allowing G'Kar to kill him. If it is the former, then accepting the Keeper was the only way to save himself and his planet from the "fire" of the fusion bombs. I can't imagine much that is worse than accepting the Keeper, so perhaps that act of selflessness is what saves him. If it's the latter, then allowing G'Kar to kill him is all that saves his planet and his soul from the "fires" of the bombs and of metaphorical damnation. If either is the case then he only saved himself on the final chance.
However, what would be interesting, and which we will never know since it would effectively be an alternate universe, is if his greatest fear was putting Centauri Prime in danger? What if he should have turned the Drakh down and refused the Keeper? Or what if his greatest fear was his death dream NOT coming true? Then it could be said that he failed on all counts.
As for the fires, I'm assuming that it is the fire of the destruction of Centauri Prime. On that count it is hard to say whether he was successful or not, since we see Centauri Prime burning on two occasions (Fall of Centauri Prime and War Without End). I think in the end it was meant to be mysterious, though I do wish we had gotten confirmation one way or the other!