So long as your Liver Disease hasn't progressed to Cirrhosis....time and abstinence should heal your Liver. However you have to be careful as there are other things which can damage your Liver...most notably OTC Pain medicines such as Aspirin, Tylenol, etc.
Are you showing symptoms of Liver Disease...is that why your doctor want's to run Liver tests on you?
If you are, and your slipping in your sobriety, you might want to check out some help from an organization like AA. The stories I have heard about people dying from Liver Disease are real horror ones....just search these boards and you can read some...scary stuff. Should be yet ANOTHER good incentive to stay sober
Good Luck