I'm really sorry to read about what happened to your girlfriend's cat. I came here because I'm really upset over the sudden death of my cat, Samantha. She also had hepatic lipidosis and was in liver failure. It does happen when cats stop eating for whatever reason. The vet said my cat had pancreatitis as well, which is what probably caused her to stop eating (diagnosed with ultrasound). If they lose a lot of weight suddenly, their livers get flooded with fat cells and fail. Very fat cats are more prone to it, but it can happen to normal-weight cats as well. It's a big reason to keep your cats trim :-( It happened so fast - just a few weeks ago, she seemed her normal self.
I went the aggressive treatment route and she had a feeding tube put it, but would still vomit. And somehow her tube was dislodged and she appeared to have choked to death. It was horrible to find her that way and i'm beating myself up with guilt: why didn't I notice sooner that she was sick, why didn't I take it more seriously when I noticed she was eating less, was I careful enough with the tube, etc. etc. I don't know if she would've made it had that not happened with the tube. She went downhill so fast.
Anyway, I'm rambling on. I really, really miss my cat. Don't let your cats get fat :-/