Sorry to hear about Luna, Kirsten. I wonder if you'd be able to get bloods from her under sedation, rather than a general anaesthetic? Sedation shouldn't be overtly risky for a 14 year old cat. Although as you say, only a biopsy will be able to give information regarding the condition of the liver itself.

It is possible to use a needle to retrieve an aspirate, or punch-biopsy, of liver tissue with the use of ultrasound to guide the vet - not sure if your vet has discussed that with you, or whether that would be feasible for Luna with sedation? It does depend on what the vet suspects is wrong with the liver so s/he may not believe it's warranted.

It's probably going to be something chronic so whether you'd prefer to know or not is up to you. There may be dietary indications for some of the possible causes, which could help lessen the disease progression but would be unlikely to reverse it entirely. Regardless, I'm sure she is currently living a comfortable retired life and will likely continue to do so for a little while yet!