personality wise, I think he'd fit in very well. Outsiders see him as cocky, but insiders say he is confident and someone who listens. They say he is a gym rat who literally spends every waking moment working on his game, despite being told about the rookie wall over and over again (he seems to actually busted right through it). Sure, he thinks he's a little thug, but he's more Space Jam than gangster. He'd fit in with Hayward who used to make rap songs called "I'm too big yo." I love players with determination and confidence, so long as they believe they still need to improve, which he does believe as evidenced by his time in the gym.
Also, those comparing Lavine to Burke are way off base. Worst case scenario is Lavine never has good enough judgement to be a PG, well then he has perfect size for an SG who can shoot, pass, and penetrate. If Trey can't figure it all out, he's just screwed as he can only pass (when he chooses to).