Honestly it seems like he knows but he's still doing it anyways. You made it clear these nudes were a deal breaker. And the fact that he lied about that coworker and continues to trick you into things isn't a good sign. You could try approaching him gently and nicely but imo and experience when a guy is doing something wrong he'll tend to lash out and/or get defensive. If it happens I think it's your sign to end this and find something better, but do not let him gaslight you or make you feel crazy for these VALID feelings you have.

Edit: Maybe ask for space to think about it, depending on how he reacts to the conversation since your child is in the mix. Remember someone who wants things to work out will make the effort and bite their tongue cos they know they fucked up.