Concerning setting in Jackson's "The Lottery," remember that setting includes what characters know, as well as what characters own and the usual things one thinks of when dealing with setting: in this case the village, the rock pile, the weather, the people, etc.
Also remember that what you know of the setting comes to you from the narrator. This means that your understanding of the setting is dependent on the narrator.
In, "The Lottery," then, the detached, somewhat objective narrator does not reveal elements of the setting that would reveal what the lottery is really all about until after you have already been led to believe that these are just normal people doing normal things. And, of course, that is the point. Normal people are capable of great violence under certain conditions.
Thus, a thesis using these ideas could read something like:
The setting, as revealed by the objective narrator, leads to the surprise ending and the horror that is created by that ending.
Or, to get back to something the narrator doesn't reveal about what the characters know:
The speaker in "The Lottery" keeps an element of setting--what readers know--from the reader in order to hide the truth of what the lottery really is.
A thesis like these would connect the setting to another vital element of the story's structure, which is what you ask for in the second part of your question.
To me, the main importance of the setting in this story is that it sets up the shock of the ending. The setting is so nice -- a small village full of nice people -- but what happens in the village is so horrible. My thesis statement would reflect that. If I were writing a thesis statement, I would say something like this:
"The idyllic setting of the small, peaceful village in "The Lottery" makes the story all the more horrible once we find out what is going on in the village's lottery."
I hope that's somewhat helpful -- good luck!