Counseling or not even salvageable??

I’ve been with my boyfriend for 2.5 years. He has cheated, talked to multiple women, lied etc the whole relationship. When we are not having issues or he’s not screwed around… we have the best relationship with so much futuristic potential it’s disgusting. But I’m sooo tired of being hurt I left. I left in January and he said all the right things to get me back. I went back in February. Now here we are and I found out he had talked to someone while we were split up(which is completely understandable and that’s not why I’m upset. I’m upset because he lied about talking to no one and then changed his story with her 5 times)…. So I got frustrated and left again. Now he’s wanting to go to counseling which is what I have been BEGGING him to do and he said he didn’t want to or he said he did but wouldn’t actually schedule it or work with me on a good date. But now he is saying he wants counseling to make this work. But I feel it’s not even salvageable?? Idk. I told him to schedule it and we would discuss things then but I wanted to still be split up because I don’t want to hurt myself anymore… do I attempt counseling with him? Do I listen to the justifications of why he talked to other women? Do I take the blame? Or just cut the ties now and throw the towel down??