I have a 3-4 page paper on the exposition of this story in which we are told to focus on the exposition on the connection between plot, characterization, and a story’s theme. I am also struggling with a thesis. any pointers?
The exposition is important first of all because we are slowly introduced to the village and the villagers. We have no idea what is really happening, and at first the story is deceptive. Everything seems normal, if not a little weird. We just think it's some quaint tradition.
There are many themes to explore in "The Lottery," but one that is fairly easy to support is the theme of how evil can result when people blindly follow tradition. So, the question is how the plot and characterization support that theme. The plot shows us what happens when people do something just because they have always done so before, and the characters certainly show us that as well.
In a literary analysis such as this one, a thesis statement should reflect the theme, which is your main point, and "list" the ways you will support that main idea, in this case, with a discussion of the plot and characters. If I were writing a literary analysis of "Sonny's Blues," for example, I might have a thesis statement like this:
The theme of darkness in "Sonny's Blues" is shown in the darkness the characters' emotions and challenges and in the repetitive use of darkness in the setting of the story.
Now the reader knows my main idea about the theme and how I am going to explicate it. Try it for your story, and you will see it's not so difficult!