What does "he got a mistress for the mistress" mean?

We don't know. Ultimately though, it's irrelevant. If you look at the script before and after that line:

Lefty: ...Whole time Sonny Black's in the can, the whole time... He's got a family, he's got a mistress. He's got a mistress for the mistress. I watched out for them, all of them. Me, I was the only one. Nobody else gave a fuck.

He's expressing frustration at how he was the only person to look out for Sunny's family. He could mean Sonny's mistress is a lesbian. He could be (and I would argue more likely is) simply exaggerating about how there were so many people in Sonny's life and he looked after all of them.

Ultimately, we don't know, but it doesn't matter - the point of the scene is to show how Lefty feels he was the only one to look after Sonny's family during his stint inside.

Does that mean he has a lot of mistresses

Yes, I think that is the most likely meaning. He has a wife, and he is cheating on her with a mistress. But perhaps there are times when he gets tired of the mistress, so he cheats on her (the mistress) with yet another mistress.

or that one of Sonny Black's mistresses is a lesbian?

That is a possible meaning, but I don't think it's likely. The movie takes place in the 1970s when lesbians couldn't get married. Also, she wouldn't really be cheating on him if he gave her another woman. So if he gave his mistress another woman, it wouldn't really be accurate to call that woman a "mistress for the mistress".