in order to introduce the paper, should I give a brief summary
Some teachers ask you to give a brief summary, and other teachers ask you to assume the reader is familiar with the story.
As a general rule, you should catch the reader's attention with an intriguing idea in the intro paragraph, and then give a brief summary in para #2. That is what I do.
Now how about that thesis statement?
Start by Googling this: Shirley Jackson, symbolism, "the lottery"
Also try this: Shirley Jackson, analysis, "The lottery"
Your thesis statement should be your own unique observation. It doesn't have to be life-changing... just unique.
:-)