I don't think she is. Her father was and she's afraid of becoming one. The alcohol in her 机, デスク was tequila. Her and bosco used to take テキーラ shots when they closed a case.
I don't think Lisbon is an alcoholic because we have never seen her drunk. Most alcoholics are drunk for a good bit of the time, and we have never seen Lisbon drunk. Who knows, maybe she wasn't trying to hide the alcohal in her desk, maybe she just has a shot once they close a case. It never implied that she was trying to hide it. I think if she was, we would know and not have to guess.