Enzyme lactate dehydrogenase catalyses the conversion of lactate to pyruvate. In this reaction lactate loses two electrons (becomes oxidized) and is converted to pyruvate. NAD+ gains two electrons (is reduced) and is converted to NADH. The half reactions involved are;
NAD+ + H+ + 2e- = NADH -0.320
Pyruvate + 2H+ + 2e- = Lactate -0.185
Giving an overall reaction of;
Lactate + NAD+ = Pyruvate + NADH + H+