Catalyzes the oxidation of L-galactose to L-galactono-1,4-lactone in the presence of NAD(+). Uses NAD(+) as a hydrogen acceptor much more efficiently than NADP(+). L-galactose + NAD(+) = H(+) + L-galactono-1,4-lactone + NADH Optimum pH is 8.5-9. Lower leaf ascorbate concentration with accumulation of L-galactose when grown under high light conditions. Belongs to the aldo/keto reductase family.