If he truly wants to change and makes an effort to then you should give him the chance to. he isn't lying to be hurtful or malicious. It's a defense mechanism so he will likely have a whole heap of personal problems to deal with which he may have not thought about for years.
If you don't feel your trust can be repaired then fair enough, but if you do then support him. Try not to take it too personally. It sounds like he genuinely wants to change.
I used to compulsively lie out of social anxiety. To get out of uncomfortable situations, to make myself seem better than I was, so I wouldn't have to open up about how I felt. Nobody got to know how i actually felt and eventually I lost connection with my emotions and didn't even know what I was feeling. It got to the stage i was really depressed and I didn't even know why it was buried so deep. I waa lying to myself about some important stuff. I had no sense of self. I didnt know who I was because all I did was lie about it.
I genuinely didn't mean for it to happen, it was hard wired into my brain and I didn't even realise I was doing it until I was confronted about it by my now husband. Nobody had known me well enough before to realise it. I completely shattered his trust and it took fucking ages before I even admitted the extent of my problem.
Eventually I began to notice myself doing it and learned to change my thought patterns from automatically figuring out the lie that would make situations easier for me and force myself to be more confident and not get into situations I'd be inclined to lie about. I.e. saying I did everything I could to get something donewhen really I'd done the bare minimum.
I had to confront some issues I'd buried really deep but I am a stronger, healthier person now and thankfully my husband began to trust me again. I'm so grateful he stuck by me. I still am figuring out who I actually am but I know now I don't have to hide behind lies.
Sorry this is so personal, I just wanted to try and give you the other side of the story and give you some reasons he might be doing it. I'm not trying to say what he's doing is OK or fair to you. Of course it isnt. but we all developing ways to cope in times of hardship and they aren't always healthy, and they often create more problems in the long run. Its human nature to cope, and every human is different so everyone copes differently.