How are the lies of black and white students different in this novel?
I would argue that the lies and plotting of the white characters aim explicitly at keeping the black characters in their inferior position, while the the black children aim at creating justice.
When Melvin and R.W. Simms, for instance, take T.J. Avery along on their robbery of the store and then fail to stand up for him after being caught, they use the prevailing stereotype of the criminal black to their advantage. They know that any white man will believe it was T.J. who robbed the Barnett store. It is also not higher science to infer that they knew T.J. might be lynched for his implication in the crime. Belittling black lives indirectly elevates the status of white ones.
Cassie, on the other hand, lies to get justice. She falsely befriends Lillian Jean, the girl whose father humiliated her after she bumped into her on the sidewalk. The false friendship is explicitly aimed at making Lillian Jean apologize to her, and thus restoring a little piece of her humanity and dignity.
All the lies are thus created and work in the framework of race.