Hi honey,
I think you need to 'fess up and tell your shrink the whole truth and nothing but the truth. Apologize for being dishonest in the past. Say that you recognize now that it was doing you no good and you need to come clean. Tell him you're coming to terms with your alcohol issues and you really don't want to lose his role in your recovery.
You're right - he might still ditch you. And that would stink. But it's not right to go on continue lying to him. He can't properly help you if you're dishonest with him. You say, "now that I'm on the straight and narrow why should I have to admit I've been lying for the past 5 years?" Because that's the beginning of how to PROVE you're on the straight and narrow - to him AND to yourself. "Straight and narrow" doesn't usually include lying to people who are trying to help you, honey.
I wish you'd still try to get to that meeting today. I think it would do you more good than you expect. I hope you feel better soon. *hugs*