Your character could need a kidney transplant. Patients whose kidneys stop working have to have hemodialysis to clean their blood. If they don't, the wastes build up and can eventually kill them. Kidneys can't be repaired, so the only way to fix the condition is with a kidney transplant. (You have two kidneys. You only need one, so when someone gets a transplant, they only get one kidney.) The condition would be end-stage renal disease.
Or the character could need a liver transplant. You don't have to be an alcoholic to have cirrhosis of the liver.
Other transplants are heart transplants, lung transplants, corneal (eye) transplants.
If you want a disease, then the person could have leukemia and need a bone marrow transplant.