And he told Molly the same thing when she 'ran into him' by the gig.

That's why Tasha still invited him in. She took it like a woman (I get it, we weren't exclusive) and he made a decision (it's done), like a man.

I'm actually curious how their characters stay on the show because without him tied to Issa, those two should disappear (outside of the, 'oh snap, I ran into Lawrence with his new chic' appeal of what, 1 episode?)

Maybe in the end he in fact reverts to wishy washy and goes back to Issa (probably after she's with some new dude, to maintain the drama) but right now, it looks like he's really moved on.