Most Helpful Guy
I'll suggest confronting him. If you don't trust him, and don't see that changing, I suggest you two break up.
The maybes are that he still wants to be friends day with his ex. I used to do that all of the time. I never thought anything of it.
Or he's still into her and wants her back, in which case I again suggest leaving.
As for him lying to her, he may be ashamed, and wants to seem like he's doing better. (could be pride, could be trying to make her regret the break-up, or again, he could want her back)
If you're snooping into his messages, stop. That is cause for mistrust on his part, and he could justify anything he's doing by saying your snooping caused it.
Most Helpful Girl
Girl that's some shit I don't like confront him. And any one talking to there ex is obviously not over them. I don't talk to my ex out of respect for my boyfriend