The main irony in Shirley Jackson's "The Lottery" occurs because a lottery is something someone generally wants to win, but this lottery results in the brutal death of its winner.
In fact, through much of the story, the lottery seems like a good thing.
The day starts off "clear and sunny, with the fresh warmth of a full-summer day" and the flowers "were blossoming profusely and the grass was richly green."
The characters, particularly the children, seemed rather excited about the event. The adults, however, seemed a bit less excited as the men "stood together, away from the pile of stones in the corner, and their jokes were quiet and they smiled rather than laughed."
In addition, Jackson clumps the lottery in with other fun social events: "the square dances, the teen-age club, the Halloween program." And these events were conducted by Mr. Summers, a "round-faced, jovial man."
All these ideas create a positive idea of this lottery the town-folk were about to conduct. But there is much foreshadowing that the term "lottery" is being used with a negative connotation. Besides the men smiling, not laughing, there are several mentions of a pile of rocks and people in the village do not want to build a new box, which suggests the idea that this tradition is something they do not want to renew.
Still, despite the foreshadowing, the reader gets to the end still believing, "hoping" might be a better word, that the lottery might be something good. This is why the moment Tessie starts shouting "It isn't fair" is shocking. Then, when "a stone hit her on the side of the head," the reader realizes that Jackson has used the term "lottery" ironically.