The stones foreshadow that someone is going to get hurt, because at the end of the story Tessie is stoned to death, because she won the lottery.
the mood is set by someone yelling "Tessie has it!" This makes the mood serious and heart racing.
The tradition is that if however draws their own name. Their whole family has to draw again to see who wins. If someone wins they are sacrificed by being stoned to death. So the community could have a good harvest.