Verbal irony occurs when words mean the opposite of their literal meaning, while situational irony occurs when events turn out the opposite from what was expected. Jackson's "The Lottery" uses both verbal and situational irony.
The title is an example of verbal irony because we normally think of a lottery as an event where a person wins a desired or coveted prize. However, in this story, getting chosen for the lottery is no prize but a death sentence, as the person whose name is drawn is stoned to death as a human sacrifice to insure a good harvest.
The first paragraph is an example of situational irony: the beautiful June day and the gathering of townspeople on the village green seems pleasant and unthreatening, giving us, on a quick read, no indication that what is to happen is anything but a happy, festive event.
Situational irony also occurs in the homey way Tessie Hutchinson arrives, almost having forgotten the lottery, and still wearing her apron and drying her hands on it. The reassuring words of her neighbor that she is still on time encourage us to believe, ironically, that what is going to occur will be pleasant.