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How old is your cat?
Does this happen when having a bowel movement or when urinating?
Is he urinating a normal amount?
Does he make frequent trips to the litter box?
Is he excessively large or overweight?
How many times a day does he have a bowel movement?
How does he act otherwise?
I wonder if he is constipated. It isn't enough that his liver enzymes are up which can result in nausea but if he is having trouble passing stool too this also can cause nausea and vomiting. If his liver enzymes are still elevated or if you are concerned about this I would consider picking up some milk thistle. This will help to treat the liver and detox it. It could also help improve bowel movements though I would recommend you use a hairball remedy for this like petromalt. Both of these are good for the liver so it won't hurt to try it.
Before biopsying the liver I would have an ultrasound performed. And if he hasn't been tested for feline leukemia or FIV then we need to do so. My biggest concern is that there may be an issue with lymphoma. A biopsy would be a good idea if these issues continue and the hairball medication is not helping.
As for the milk thistle: your vet should have a product called denamarin or at least he can order if for you. This contains both SAMe and milk thistle to help the liver function better.