Catalyzes the conversion of lactate to pyruvate. (S)-lactate + NAD(+) = H(+) + NADH + pyruvate The quaternary structure is constitutionally similar to the active conformation of allosteric LDHs, and the regulation is independent of the fructose 1,6-bisphosphate-binding site. Fermentation; pyruvate fermentation to lactate; (S)-lactate from pyruvate: step 1/1. Homotetramer. Belongs to the LDH/MDH superfamily. LDH family. Was originally (PubMed:1840590 and PubMed:1425707) thought to originate from L.plantarum.