as well as the above:
blood flowing through the muscles transports lactic acid to the liver, where lactic acid is converted back into glucose
the glucose produced is supplied to the muscles in the bloodstream; muscles can use oxygen in the blood and glucose from the liver for respiration.
then, when the oxygen and glucose have been completely converted to carbon dioxide and water, the oxygen debt will be repaid since there is no lactic acid left, and the muscles can respire aerobically, releasing more energy.
hence, the liver helps to restore aerobic respiration in the muscles, which may be why it can be counted as an organ of respiration.
hope this helped!