While the easiest way to approach the cultural aspects of "The Lottery" is to look at the connection between the story and the persecution of Jews in Germany—completely decent-seeming people doing atrocious things—the story also calls to mind traditional elements of mid-20th Century America, particularly the treatment of blacks and women in the country. However, the theme of scapegoating based on tradition is universal.
In "The Lottery," Shirley Jackson creates a village that is full of kind, if not a little bit strange, people. They are polite to one another ("[The women] greeted one another and exchanged bits of gossip as they went to join their husbands."). And they seem to believe this tradition of stoning people to death in order to encourage their crops is somehow progressive ("Listening to the young folks, nothing's good enough for them. Next thing you know, they'll be wanting to go back to living in caves, nobody work anymore...") Yet this activity of stoning a person to death in order to encourage their crops, if that's what the lottery really is meant for, represents the kind of thinking that says, "This is the way things have always been done" and that change would bring about social disorder.
This theme could be applied to any mid-20th Century issues: if African-Americans gained equality through civil rights, traditional America would be in disarray; if women went to work, traditional American families would be destroyed; if the Communist Party or even Communist thinking became part of the political process, America would be destroyed.
The universality of this story's major theme is why it bothered so many people when it was published. It forced the public, subconsciously at least, to think about their traditions and how many of these might be harmful to others.