My BF was also a reformed alcoholic who fell off the wagon a few years ago due to serious stress in his life. During this period he also became a big liar. He told a zillion lies about everything from his health to his day to day activities. He is a secret drinker and a 'top up' drinker, but you would never suspect he was drunk.
Like you, I knew nothing much about his background, and it was a new friendship. Eventually, on moving in together he would act very secretively and I could never pin down why - ofcourse later on to find out alot of it was the drink.
After hitting his rock bottom (this time) he has now quit again. He has been sober for nearly 18 months (Im so proud!).
But the lies continued long long after the drinking stopped. Lies about other things but do seemed to have stopped now.
Its very difficult to trust again, and I have to be wary that Im not being paranoid, but I do notice that he is, in general, a secretive man. But I have had to learn to trust and respect his privacy and just hope that whatever he needs his privacy for it is not to the detriment of our relationship.
I feel i would be able to spot the drinking again this time as I am now far better clued up to it than before,(but boy he was clever at hiding it) but he will do things that make me suspicious - with things that I had never really had any cause to be suspicious over (like password protect his pc but insists he has nothing to hide
and then tell me I am the paranoid? To which i just told him, if he has anything to hide, im sure it will come out - as it always has!
Perhaps not the best way of having a relationship, but trust does take an awfully long time to repair.
So from my personal perspective, I do think that the secretiveness that has to be undertaken in order to try to maintain a longer term lifestyle whilst drinking heavily, can sort of, become a habit.
But not one that cant be overcome.
At least he has been totally honest with regard to his drinking problem and you are wise to look into it. I hope he is able to open up to you and as you get to know him better, you need to be able to ask about anything that you have doubts about.