I speak from my personal experience, no matter what effort you put in, your LG will think he is right to go out. The more effort you put in, the more he will think that way.
I saw a lot of couples going on this pattern in my family or neighbour during my growing up. When I got married, I was fully ready to divorce anytime. But after so many years, my wife and I still enjoy each other. The reason is simple, we know the consequence, so we both comprise. Once upon time, I had feeling to other woman, but I could understand, this was just some attraction from fresh flesh, it would soon fade out, not worth to give up what I have.
LZ must understand whether your LG can realize what is real marriage means, what is value the marriage brings in. I bet he can not. From what I observed during my growing up, none of those couples had happy ending. So divorce is your only chance, although it is very slim, that your hu*****and may wake up after he stays with the other woman for a while and the fresh feeling fades. If no divorce, your LG will always image what a wonderful world it could be he was with the other woman.