What is ironic about the conversation in "The Lottery"?
It is ironic that Tessie protests her own selection when it is probable that she has participated in these lotteries and executions before. It is also ironic, as noted in an exchange between her and Mrs. Delacroix, that she almost missed the lottery because she forgot that it was the 27th. There's even an exchange between Mr. Adams and Old Man Warner about some towns giving up the lottery, but they dismiss that as the crazy notions of young people who do not appreciate the traditions of their elders.
The most ironic part of all is an exchange between the townspeople in general as they discuss things such as the weather, their farms and taxes when they are about to commit a ritual human sacrifice. They don't regard stoning as barbaric--they consider themselves "civilized."
In Shirley Jackson's "The Lottery", the conversation takes on an ironic tone in at least two places. One is the commonplace tone of the talk of taxes and everyday life when a death is imminent.
Perhaps more ironic is that Mr. and Mrs. Adams casually suggest that it may be time for the community to quit lotteries with one of them even adding that some communities have already quit. They are, of course, opposed by Old Man Warner who says there has always been and should always be a lottery. Ironically, the text points out that both the Adams couple and Old Man Warner are up front participating in the communal stoning of Tessie.