No, the liver cannot convert fat to amino acids, since their compositions are entirely different. Fat, however, can be hydrolyzed by lipases to their respective glycerol and fatty acid components. Glycerol can then be converted into PGAL, and fatty acids can be converted to acetyl CoA, both intermediates of cellular respiration. The only way you can get amino acids I believe, not entirely sure, are from proteins. Once the proteins are broken down into amino acids, the amino acids can undergo transamination reactions (loss of an amino group to form a-keto acids) and can eventually form acetyl CoA, pyruvate, or some other intermediate of cellular respiration. Hope that helped!