Catalyzes the NADPH-dependent reductive condensation between pyruvic acid and the side chain amino group of L-ornithine to form N(5)-(L-1-carboxyethyl)-L-ornithine. To a lesser extent, can also use L-lysine as substrate (yielding N(6)-(L-1-carboxyethyl)-L-lysine). NADH cannot replace NADPH in the condensation reaction. H2O + N(5)-[1(S)-1-carboxyethyl]-L-ornithine + NADP(+) = H(+) + L-ornithine + NADPH + pyruvate Is potently inhibited by the reaction product N(5)-(L-1-carboxyethyl)-L-ornithine. Optimum pH is 8.0. Active over a broad pH range of 6.5-9.0. Stable to heating at 50 degrees Celsius for 10 minutes. Rapidly inactivated by heating at 60 degrees Celsius. Homotetramer. No enzyme activity is detectable in the reverse direction with NADP(+) and chemically synthesized N(5)-(L-1-carboxyethyl)-L-ornithine as potential substrates. Belongs to the AlaDH/PNT family. CEOS subfamily.