The title of this instrumental piece probably refers to excessive alcohol consumption over many years, which is a leading cause of liver disease. It brings to mind those things our mothers might tell us when we're young. Too much alcohol can make a normal liver swell with fat, causing a condition called fatty liver. If the fat becomes inflamed, it can lead into either alcoholic hepatitis, a liver problem that causes serious but often reversible liver damage, or cirrhosis, which causes irreversible liver damage.
This title could also be a play on "liver", as in "one who lives life", and is evoking all those factors that contribute to decay in one's life.
The actual term "Liver Rot" a.k.a "Black Disease" is a term from veterinary pathology originating from 1910-15. It's an acute, usually fatal disease of sheep caused by general intoxication from Clostridium novyi, an anaerobic organism that multiplies in parts of the liver damaged by the common liver fluke.