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. . This is the function of LDHAL6A (lactate dehydrogenase A like 6A, ENSG00000166800).