The central irony in Jackson's "The Lottery" is that normal people are capable of great brutality when that brutality is sanctioned by the majority or by society.
The irony is developed through the use of point of view, setting, character behavior, and foreshadowing.
The limited point of view reveals only what appear to be everyday, normal details. The village appears normal (school has recently let out, the kids think of school, people are in a hurry to get to lunch, they gather for a summer festival of some kind), and no thoughts are revealed. Thoughts, of course, would give away the surprise ending.
Foreshadowing makes the surprise ending make sense, once it occurs. The boys gathering stones, for instance, seems harmless at the time, but gives the ending legitimacy.
The irony only becomes apparent when the nature of the lottery is revealed, though. Thus, it isn't that irony develops the story, but that the story reveals the irony. In some works, the irony does develop the story. In this case, however, the irony is revealed at the conclusion of the story.