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 29 sec(-1) with NAD(+) as cosubstrate. kcat is 2.2 sec(-1) with NADP(+) as cosubstrate. Deletion mutant is unable to use L-threonate as a carbon source. Belongs to the HIBADH-related family. L-threonate dehydrogenase subfamily.