Irony of Target Audience
Fairy-stories have traditionally been associated with children; they are typically seen as fantasy stories that teach children to use their minds, but that have no real value beyond the imagination, having no significance for adults and those who live in "the real world." Tolkien, however, directly argues against this assumption, saying that fairy-stories have perhaps even more significance for adults, who need "a recovery of clear sight" after being inundated in this fallen world. Fairy-tales, ironically opposite to popular conception, have enormous significance for adults as well as children.
Irony of Escapism
A common accusation against the fantasy genre is that it is escapist, allowing people to escape this world and live in another one, neglecting the importance of responsibility in this world. In his treatment of the issue, Tolkien ironically doesn't actually disagree with this assessment, instead arguing that escapism is a good thing, as this world is broken, and we need to escape it from time to time to remember what is beautiful about it as well as to look forward to the eventual transcendence of mortal life. As Tolkien says, participation in escapist literature is not "the flight of the deserter," but "the escape of the prisoner."
Irony of Fairy-Tale Collections
When writing on fairy-tales, one might expect Tolkien to look back on traditional fairy-tale collections, such as those of Andrew Lang and the Brothers Grimm, as primary examples of the highest form of the genre. Ironically, however, Tolkien takes issue with these founders of the genre, arguing that their collections are mostly full of worthless material, although there is occasionally good fantasy hidden away in there somewhere. Lang he praises more than the others, but he still finds great fault with all of these 'predecessors.'
Irony of the Andrew Lang Lecture
This essay was originally given as the keynote speech for the Andrew Lang honorary lecture at the University of St. Andrews in 1939. Ironically, instead of agreeing with Lang, Tolkien argues against his ideals and methods, saying that his collections are like stalls at a garage sale - there are some valuable items, as the seller has identified the best parts of his possessions, but it's still mostly a mish-mash of rubbish.
Irony of Faërie
Faërie, as Tolkien explains, is the imaginative "perilous realm" that is home to all true fairy-stories. He says, however, that it is impossible to actually describe Faërie, which is inexplicable yet not imperceptible. This irony is particularly striking because Tolkien's essay is ostensibly an attempt to define fairy-stories, which he defines as stories set in Faërie, but further explanation is suddenly cut off because Faërie is itself indescribable.