(R)-N(6)-dihydrolipoyl-L-lysyl-[protein] + NAD(+) = (R)-N(6)-lipoyl-L-lysyl-[protein] + H(+) + NADH Binds 1 FAD per subunit. The active site is a redox-active disulfide bond. Belongs to the class-I pyridine nucleotide-disulfide oxidoreductase family.