Catalyzes the reduction of sulfopyruvate to (R)-sulfolactate much more efficiently than the reverse reaction. Also catalyzes the reduction of oxaloacetate, alpha-ketoglutarate, and to a much lower extent, KHTCA, but not pyruvate. Involved in the biosynthesis of both coenzyme M (with (R)-sulfolactate) and methanopterin (with alpha-ketoglutarate). a (2S)-2-hydroxycarboxylate + NAD(+) = a 2-oxocarboxylate + H(+) + NADH Cofactor biosynthesis; coenzyme M biosynthesis; sulfoacetaldehyde from phosphoenolpyruvate and sulfite: step 3/4. Cofactor biosynthesis; 5,6,7,8-tetrahydromethanopterin biosynthesis. Belongs to the LDH2/MDH2 oxidoreductase family.