Hi Tex, welcome, and of course it's OK to post! This site is here "to discuss our progress and to support and inform those who are new to the process", or in other words to help each other.
Sorry to give the pseudo-legal spiel, but it does matter because it's true

- I am not medically qualified in anyway, and my opinions are purely those of a layman, so please don't treat them as anything other than such.
I'm unaware of any studies looking at interactions between Naltrexone and pre-existing liver disease. My limited understanding of the oft-quoted figures of 50mg therapeutic dose and 300mg "that your liver can stand" leads me to believe that Naltrexone actually has a fairly poor therapeutic window in healthy individuals.
When starting Nal some 5 months ago, my liver functions were mildly out of range (GGT specifically); since then, they've returned to normal range because of the lower booze intake. I'm also taking an anti-fungal which has possible hepatotoxic side effects, though I stopped taking that whilst I started Nal.
In summary, I think Hesster hits the nail on the head - keeping on drinking will cause worse damage than Nal, though I'd also add that (in my opinion) you're right to be concerned. Roll on Nalmefene

. How much experience does your doctor have with prescribing Nal? If they've got a lot then they'll almost certainly have a feel for it; if they don't, then you could get them to talk to a hepatologist and "ask around" the medical community to get a proper answer.