Welcome to the point of the entire novel. In Roll of Thunder, Hear My Cry, the African-American characters have to persevere against many kinds of injustice caused by the racist oppression in the South during this time. From small injustices, like being ignored in the grocery store in favor of white people, to much more serious ones, like being burned alive for speaking to a white woman, part of building character and growing up in this novel is learning how to cope with these injustices while retaining your self-respect and dignity.
Cassie shouldn't have beaten up Lillian Jean. Her actions are a form of "vigilante justice," and similar in kind (though certainly not degree) as the Wallaces.
Lillian Jean gets exactly what she deserves from Cassie. After all, Papa said that Jesus advocated "turning the other cheek," but that he didn't mean to be a fool.