When the muscle is exercising, and only anaerobic respiration is done, pyruvate -> lactate to regenerate NAD+. Lactate is then transported out of the muscle and into the liver, to regenerate glucose, which is then shuttled back to the muscle (the Cori cycle).
I was wondering whether once the muscle stops exercising, the muscle itself could regenerate pyruvate (using lactate dehydrogenase), or whether muscles always release their lactic acid to the liver? Or maybe there is no way of knowing this (how would this be tested experimentally...).