From my own experience, I kind of have the "does it matter?" mentality that hopeful stated up top. In active addiction people are not in their right minds. They display all kinds of whack a doodle behaviors. My husband was becoming really, really abusive towards me near the end of his downward spiral but had never previously exhibited that kind of behavior towards me. He also lied to me. A LOT. But if I'm being honest, the lying has always been there and I just accepted it until it was coupled with all of this other crap.
Whether he's got some kind of mental illness (BTW, I think addiction in and of itself is plenty to ascertain that someone is mentally ill) is really outside of my hoola-hoop. I'm more interested in understanding why I've accepted lies in the first place and what I can do to make sure that I don't accept such crappy treatment in the future and to refuse that behavior in a rational and loving way (mostly loving towards myself).
If your daughter has a mental illness, what can you possibly do about it? Hint: you cannot make her do anything. IMO, this keeps the focus on the alcoholic - whom you cannot control - rather than healing yourself.