Considering William Golding's Lord of the Flies as a whole, the greatest irony is that the boys, who escape war and death by their saving arrival on a paradisiacal island far removed from the "evils of society" degenerate into worse creatures than they would have become if they had remained in their homeland.  For the "evils of society," ironically, lie within the human heart; evil is inherent in man, the "beast" is he, as Simon discovers.  So, just as in the Garden of Eve where it is Adam and Eve who commit the evil act, so, too, is it in Lord of the Flies.  Interestingly, Golding eliminates any Eve from the situation to prove that the evil is inherent and not caused by any temptress or anyone else that can be blamed.  As the Lord of Flies hangs in space before Simon, it says,

'Fancy thinking the Beast was something you could hunt and kill!' said the head.  For a moment or two the forest and all the other dimly appreciated places echoed with the parody of laughter.  'You knew, didn't you?  I'm part of you?  close, close, close! I'm the reason why it's no go?  Why things are what they are?' 

I'm not sure whether you mean irony in the novel or irony in the symbol "The Lord of the Flies."  In the novel there are many ironies:

(1) The initial fire that was supposed to be a rescue fire results in the probably death of one littlun with the birthmark.

(2) The adult sign that Piggy and Ralph long for comes in the form of a dead parachutist that creates even more havoc on the island.

(3) The adults that Piggy and Ralph think are "having tea" and "discussing things" are actually engaging in a world war themselves.

(4) The fire that was supposed to smoke out Ralph so that Jack's tribe could kill him results in Ralph's (and the boys') rescue.

(5) The naval officer's "rescue" of the boys is from one warring place to another. 

(6) The boys' greatest threat was not an external one as they believed but themselves.