What Old Man Warner represents in the Lottery is blind tradition. What I mean by this is willingly accepting an outdated tradition just, because that's what people before you have done. Old Man Warner knows that the tradition is unfair, but proceeds to keep the tradition going.
Tone and Theme
"The black box grew shabbier each year; by now it was no longer completely black but splintered badly along one side to show the original wood color..."
The setting being a clear sunny, fresh and warm summer as the day someone is going to die is situational irony.
How corrupt and unfair society treats women where all men decide who is the next person to "win" the lottery while the women have to let their fate be decided for them and not by themselves.