What are the main ideas and supporting details of "The Lady, or the Tiger"?
This sounds like a loaded question. I suppose what you (or your teacher) are driving at is that the story line itself is supporting evidence for the hypothesis that anybody can commit a violent act if driven to it. "The catalyst" in this story triggering an act of violence would of course be jealousy, tempting the princess to sacrifice her lover in the arena rather than see him "taken" by another woman.
Whether she actually did it or not is left to the reader's speculation and contemplation.