There are three main types of irony--verbal, situational, and dramatic.
Verbal irony is the use of words conveys something different than the literal meaning (essentially, when one says something and means something very different). An example of this is a parent telling a child that the child did great on a test when the child scored an "F."
Situational irony is when the outcome is the opposite of what is expected. For example, a fire truck catching on fore is situational irony.
Dramatic irony is where the audience (reader or viewer) knows that something is going to happen and the characters do not. For example, a villain is hiding in the closet and the home owner is getting ready to open the door (and the audience knows that the villain is in the closet).
The identification of irony included in Shirley Jackson's "The Lottery" depends upon the reader. For example, if a reader can identify the foreshadowing of the collecting of stones by the children, the reader can, then, identify the irony as dramatic. As for the irony depicted in the setting, the townspeople, and the lottery itself, different irony can be identified.
The setting of the town--The town is idyllic. It is summer, and the flowers are blooming. Given the peaceful and beautiful setting, one would not expect the townspeople to murder one of their own. This is an example of situational irony.
The townspeople--The townspeople seem to be caring and concerned people. They gather together in conversational groups, steering clear of the pile of rocks the boys have made. Once the "winner" of the lottery is drawn, the townspeople immediately attack Tessie. This is an example of situational irony (unless the reader knows what is going to happen, then this would be identified as dramatic irony).
The lottery--The lottery today confuses many readers about what may happen in the story. Most believe that the lottery is something good. Therefore, this is an example of situational irony.