It's a very tough position you are in, honeypig. Your relationship with him is "functional" in the same way that some alcoholics are "functional." The surface presentation is working, but underneath there is ongoing decay.
He has been progressing in his addiction, and he is likely quite physically dependent on the alcohol, in addition to the emotional and psychological dependency. He lied because he is afraid to give it up. Unwilling to give it up. Not yet desperate to give it up. And perhaps physically he cannot give it up. He has an intense bond with alcohol, and it is destroying the bond he has with you (which, it seems to me, is there, even though badly damaged).
People who enter recovery enter those rooms flat-out near dead. They are sick, they are hopeless, they are scared out of their minds. The ones who are the worse off are the ones who probably want recovery the most. And when they hit that final bottom, and go crawling into the rooms, they work a program. They hit several meetings a week, usually daily, for months, they get sponsors, they get counselors, they are 24/7 recovering alcoholics while they are trying to scrape themselves off the floor and clean up the wreckage of their past and present.
When you say he is "apparently" on the wagon, I have trouble believing he is sober at all. Addiction is so powerful. Alcoholics don't just put it down. Those who merely abuse alcohol for years can do that because they aren't addicts. But addicts are BONDED to the drink and they have an overwhelming compulsion which causes them to drink against their wills. Reading chapters 2 and 3 of the AA Big Book at
Big Book Online Fourth Edition helps make this very clear to those of us who do not understand the experience of addiction. So when someone is in recovery, there seems to me there would be no mistaking what is happening.
To file papers for divorce as a reaction to his drinking and lying is a deeply emotional response to a very complex situation. If you can give yourself perhaps six months to sort things out in your mind and heart, you will have given your Higher Power opportunity to work in you, to reveal more of what you need to know in this crisis and cannot yet see. Your AH is not abusive. He is certainly unavailable for relationship. He is certainly consumed. But your words indicate he is not abusive. So if you go to Al-Anon (2 or 3 meetings a week) and work with a sponsor for perhaps six months, you can buy yourself some time so you can make good choices with a clearer head.
He will perhaps continue to drink throughout this period of time, and though it will at times hurt you or make you angry, there may come a day, with your work in Al-anon, that you realize you are not nearly as reactive as you once were. This does not mean you want to be married to an unavailable man. It means that if the day comes when you need to leave, you will do so with much less bitterness than if you had not given yourself the time to find your center and examine your needs.
Years ago I was an Al-Anon member in Akron, Ohio where AA was founded by Bill W. and Dr. Bob. I lived very near the mansion where they were introduced to each other as a result of Bill W. asking the mistress of that mansion if she could find him another alcoholic to talk to to help him stay sober. Both those men got sober and millions more since then have done so. The Al-Anon meeting I went to was very strong. And there were women there who had long marriages to alcoholics, and the alcoholic and the wife had each entered their respective recovery programs and they had each taken an individual journey--sometimes living separately, or sometimes just splitting the house into "private" zones--and because they had done the work and were continuing to do the work, they were not only still together, they were bonded. Once broken, they had rebuilt their lives, separately at first, and then later, as a couple.
So if you would like to first do your part, in Al-Anon, and then examine the marriage with a better perspective coming from greater self-awareness, then I would try the program for several months and see what happens. Have no expectations of him. This would be about you.
If it were me, I'd tell him to live up there in that attic until you make up your mind how you wish to live your life.