I think he plays himself that way on the show. He's very funny but improv wise he's not in the tier with JB, Jeff, Susie, Richard Lewis. It may be because he doesn't know Larry as long as the others, so I think he plays that way.
Susie said irl that she has never discussed her character with Larry so I would think he leaves it up to them.
I don't need to be too high minded but the show sounds like a ton of work. I'm always impressed when they break each other up because you know it's a gem.