Interconverts simultaneously and stereospecifically pyruvate and lactate with concomitant interconversion of NADH and NAD(+). (S)-lactate + NAD(+) = H(+) + NADH + pyruvate Fermentation; pyruvate fermentation to lactate; (S)-lactate from pyruvate: step 1/1. Homotetramer. Interacts with PTEN upstream reading frame protein MP31. ISGylated. Belongs to the LDH/MDH superfamily. LDH family.