Catalyzes the oxidative deamination of L-lysine in the presence of NAD. Can also use (S)-(2-aminoethyl)-L-cysteine as a substrate, but more slowly. Can use both NAD and NADP but the preferred substrate is NAD. L-lysine + NAD(+) = 2 H(+) + L-1-piperideine-6-carboxylate + NADH + NH4(+) Optimum pH is 10.1. Optimum temperature is 70.0 degrees Celsius. Homohexamer. Belongs to the saccharopine dehydrogenase family.