First, you need to select the two stories that you are most comfortable discussing. Because I do not know which two these are for you, I will use “The Lottery” and “Two Kinds” as an example.
The stories are different stylistically and thematically. However, both concern tradition and pressure from an external source.
In “Two Kinds,” the narrator feels as though her mother always tries to control and change her, wanting a genius prodigy for a daughter. The narrator eventually decides to rebel against her mother’s influence at the expense of her mother’s feelings. The mother feels pressure for her daughter to be talented and successful because of her friend Lindo, whose daughter is a chess prodigy, and a desire for the American dream. As a result, the mother exerts pressure on the narrator, who doesn’t share her mother’s aspirations. Her mother also thinks it is important for her daughter to be the right “kind,” or the obedient kind. She wants a traditional Chinese daughter with a prodigious talent.
In “The Lottery,” the villagers all seem to honor the tradition of the titular harvest ritual despite how it makes many of them uncomfortable. The tension prior to the commencement of the lottery shows that many of the villagers likely don’t enjoy the game, but they tolerate it because they have always done it. The winner, Tessie Hutchinson, expresses how unfair it is—but only after realizing she will be the one to die. This shows that society’s long-held traditions are firmly rooted in a culture, and it takes more than a single protesting individual to overcome them.
For your thesis, I would suggest talking primarily about how a thematic idea is developed over the course of both stories that you select. For the two mentioned above, that thematic idea is tradition. To analyze these, you could discuss how society influences these traditions or goals. You might also consider character development (Tessie, mother, daughter) to help make your points.