How about going for walks yourself now, and inviting him occasionally? Instead of waiting for him to invite you.
And it SHOULD be hard for you to accept its over. He's already lied to you a couple of times about it previously. It will take time to trust him again. That isn't anything to feel bad about. Even if he'd not liked previously, it would be hard - but he hasn't been terribly trustworthy, and he still has feelings for her. So just allow yourself the time you need to build up trust again.
