Catalyzes the interconversion of L-lactate and pyruvate with nicotinamide adenine dinucleotide NAD(+) as a coenzyme (PubMed:18351441). Significantly increases the transcriptional activity of JUN, when overexpressed. (S)-lactate + NAD(+) = H(+) + NADH + pyruvate Fermentation; pyruvate fermentation to lactate; (S)-lactate from pyruvate: step 1/1. Testis-specific. Belongs to the LDH/MDH superfamily. LDH family.