I think you and only you have to decide what you are willing to accept and not accept from the relationship. Some people can live with one infidelity, or even more (think of Hillary Clinton)--it sounds like you are NOT one of those people, given what you said up front in your post about cheating being the line in the sand for anyone you have a relationship with.
It is possible to adjust those boundaries and accept him for who he is, I suppose--accept that he will probably cheat again, and will certainly lie to you (he made a point of saying he doesn't lie, and then committed the ultimate lie). If you get from the relationship so much that it balances out the fact that he is a manipulator, a liar, a cheater, continue with the relationship.
Also, I hate to say it, but 10 years of sobriety doesn't mean that much--he is still one drink away from being an active alcoholic. Not to demean his sobriety and the wonderful accomplishment in sobriety he has maintained at all--but you, like him, will have to accept that blessing just one day at a time and not pin your future on it.
If anything happens to my relationship with my AH, I personally would rather not go into a relationship with anyone who has ANY history of alcoholism--I've gotten too many bumps from falling off the wagon with all the As in my life. And I do know lots of absolutely wonderful RAs... I've just been burned too much.