Lillian Jean is Cassie's mean-girl antagonist. And Cassie may be biased as a narrator, but LJ doesn't sound too cute: she's "scrawny, chicken-legged, [and] snaggle-toothed" (6.80).
Where Jeremy would like to be friends with the Logan children, Lillian Jean wishes they would drop off the face of the earth. She goes to no trouble to hide her contempt for the African-American children. Check out what she says to Cassie when Cassie accidentally bumps into her:
You can't watch where you're going, get in the road. Maybe that way you won't be bumping into decent white folks with your nasty little self. (5.88)
She gets a nice taste of payback for humiliating Cassie when Cassie hatches a plan to behave like her "slave." After many weeks of duping Lillian Jean into believing Cassie is truly her friend and willing servant, she lures Lillian Jean out into the woods and has a go at her. With fists. After whipping her pretty good, Cassie wrests an apology out of Lillian Jean, in exchange for the humiliating one that Cassie had to give her in the street in Strawberry. And what an apology it is. Lillian Jean is a sort of stand in for all of the white people and everything they should be apologizing for (but aren't):
And she apologized. For herself and for her father. For her brothers and her mother. For Strawberry and Mississippi, and by the time I finished jerking at her head, I think she would have apologized for the world being round had I demanded it. (8.84)
But the thing is, we're not convinced. Lillian Jean may apologize, but she doesn't seem to understand why she has to apologize. She's confused that Cassie's doing this—and we think that this might be one lesson that's never going to be learned.