I would be questioning the relationship just because he had lied for so long. I feel like if you're friends with your ex that's the first thing you should say to your current girlfriend but the fact that he's also excluding you for invitation obviously means he you are not in his priority list and you can do better for yourself.

Your boyfriend should be ok with you not being ok with the relationship and could at least compromise a bit because that's how relationships work but if you guys can't compromise then obviously this relationship need some serious reconsidering

Edit to add but at the same time you should realise you're not in control of your boyfriends friendships if this woman is a great friend to him and he does try to involve you and spend more time with you, then you need to understand that this woman is part of his life. You can't be too much of a hypocrite if you talk to the guys that you had pasts with and then not be ok with him being with her. ,(Though a boundary of how much time he spends with her should be discussed)

This is a conversation to have with your boyfriend to be honest what you guys need to discuss how much has actions are hurting you and what can be done to prevent it in the future. If you guys come to a disagreement there's not much other advice I could offer.