The asshole part rings true. Those types tend to not be very popular so they keep close the ones that stick around. I imagine Lucille must have been quite the treasure to him. Losing someone like that would be devastating for anyone. Raven can relate to that. I think she'll assume that the bat was named after someone that was very dear to him. She'll ask but won't prod. Everyone deserves their privacy. Even assholes.
We'll see how far she gets with him. She'd definitely be softer towards him once she knows more about him and what he lost. I can see her giving him advice as well about how to run things, even if he doesn't want or need it.
They're all survivors. Anyone who's lasted this long will be. Or incredibly lucky. He's got the right idea, even if he goes after it a bit differently than most.