I think you should tell them about the Lie for one reason.... the Lies will get bigger and more personal if you dont stop drinking.
I am the same way except for the fact that I am married and I lie to My wife about my drinking and whatever else makes me sound the way i INTEND on being.
So my take:
If you confess that little harmless lie and quite drinking it will be hard for you to tell the next lie.
I too would like to know why we lie! My wife is very cool and understanding. She always told me that she didnt mind the drinking as much as the lying. We would have that discussion while sober and I would be so determined not to Lie and hide my empty beer cans and wine bottles all over the house. But as soon as I got a good buzz I would start planning my nest lie.
My wife does not understand our problem and started looking at me as a lair. I decided that I would rather be a recovering alcoholic than a lair.
Trust me.... the lies will only get worse so stay sober.