NADH is oxidized anaerobic conditions by lactate dehydrogenase because in order to transform or change Pyruvate into Lactate it has to happen in an anaerobic condition that is where we hardly find oxygen(in the presence of no oxygen).
The chemical compound or say the enzyme known as lactate dehydrogenase gets its proton from NADH( in a REDOX type reaction). After getting the proton from NADH, it uses that to convert Pyruvate into Lactate.
NB: the conversion can also be done in aerobic condition but more ATP will be produced. With anaerobic condition, less ATO is produced and there is re-oxidation.
