Are lighter urine and increase in energy and appetite levels signs of recovery from liver disease?

May be: Jaundice (yellow pigment) in the skin accompanied by dark urine, light color of stool are classical signs of liver problem. These signs become less obvious as the liver function improves, so the lighter urine and increased appetite suggests recovery; however, it is best to check liver function studies to assess what is going on.

Not specific: These signs are not specific enough to be taken by themselves as signs of recovery. One might expect to see them in the recovery phase of acute hepatitis but the real indicator would be improvement in blood tests. Some forms of liver disease might require biopsy to prove ultimate improvement or remission. Don't take these signs as a green light to not having to be concerned. See your doctor.