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 kcat is 28 sec(-1) with NAD(+) as cosubstrate. kcat is 3.5 sec(-1) with NADP(+) as cosubstrate. Belongs to the HIBADH-related family. L-threonate dehydrogenase subfamily.