I feel like I need to chime in only because sometimes they do recover and change, although it's not the norm. I've heard 10%. My RAH (5th year of sobriety) says that he's unsure if that's accurate because so many people leave their programs but later find other ones so they aren't tracked.
So let's say 10% recover. Those aren't great odds and if I started a relationship built completely on lies I don't think I'd stay.
My husband lied to me all of the time while he was drinking, about big things and small. For me, the hardest part about being with an alcoholic was never being able to trust what he said about any stupid little thing. When he finally got sober (after a billion attempts) it took a year to start trusting him and then a couple to stop doubting him.