Catalyzes oxidation of L-threonate to 2-oxo-tetronate. Can use either NAD(+) or NADP(+) as cosubstrate, with a preference for NAD(+). L-threonate + NAD(+) = 2-dehydro-L-erythronate + H(+) + NADH Belongs to the HIBADH-related family. L-threonate dehydrogenase subfamily.