It might be too niche because I don't think there are many fans of both Bones and Lie to Me out there.
However, I was thinking about a possible crossover in which Cal and Brennan would obviously not get along. Just imagine those minds fighting! However, Booth and Gillian would get along very well. Booth thinks Gillian is a smart, fine lady, and she thinks he's an honest, hardworking FBI agent.
I imagine them changing cards after the case and talking about their "crazy brilliant" partners. They would understand each other and the love they have for their respective partners without saying much.
If I were to push it, I would say that they would stay in touch and that Gillian would be a soft, nice aunt to Christine and Hank (Gillian with kids <3). Eventually, Brennan would learn to love Gillian as well. An extra kind and patient soul in her life was not in her cards, but she would accept it.



















