I might hazard a guess that "don't put pressure on your liver" means don't take medications that might tax the liver, or drink alcohol, etc. I don't think they meant "don't squeeze the liver."
However, if they did mean that, it would be my recommendation that she sleep in the left lateral decubitus position.
Since the liver is on the right side, lying on her left side with the head of the bed slightly elevated will exert the least amount of pressure on the liver. Probably the next best thing would be on her back with the head of the bed slighty elevated.
I did find one paper addressing the position of the body in the treatment of various illnesses, calling the role of position in treatment "postural medicine". Much of this is common sense (that is, experience has taught us as much) but some of it is new to me.
The role of body position and gravity in the symptoms and treatment of various medical diseases.