Two symptoms of liver compromised dogs are coat and/or skin issues. That said, I feel you will have a difficult time finding the exact diet to see improvement in her coat, as her liver isn't processing and storing the nutrients she needs to maintain a nice coat at this time. I would be more concerned about the amount of toxins in her system and work towards limiting those, as that may be more of a help to her liver and overall health than anything.
Generally speaking, dairy and vegetable proteins are recommended for LS dogs, bc they require less processing by the liver and do not cause the amount of toxins to be produced during digestion as meat does. Hard boiled egg whites are what I have found listed in special diets for LS dogs, but as for amounts you would have to check with your vet, as other facters such as her size and weight need to be taken into consideration. There are diets listed on several sites dealing with LS, such as:
Liver_Shunt_And_MVD_Support : Liver Shunt & MVD/HMD Support DogLiverDisease : Dog Liver Disease Liver Shunt The University of Tennessee College of Veterinary Medicine - Liver Shunt Research http://www.vet.utk.edu/clinical/sacs...Liver_diet.pdf