The last line of "The Lesson" is "But ain't nobody gonna beat me at nuthin." This has a few closely related meanings. First, of course, the local and literal meaning: the narrator (Sylvia) isn't going to let Sugar beat her at running, no matter what. Second, and more importantly, Sylvia has learned a more general lesson through the events of the story. She isn't going to let anyone beat her, which also means, she's not going to accept being poor, or being considered second class in any way. Sylvia has reached a point where she's committing to shaping her own destiny. That's the biggest lesson of the story.