Is one of the functions of the lymph to drain deoxygenated blood from the tissues and return it to the heart?
Not quite, the lymphatic system drains the fluid carried with the blood (the lymph) back to the heart that has ‘leaked’ out as the blood passes through the capillary beds.
The normal way for deoxygenated blood to be returned to the heart is through the veins.
The exception to this is if you have sustained tissue damage (a bruise) that causes blood to leak into the interstitial spaces between the cells.
Just so you know, one artery in the body also carries deoxygenated blood (the pulmonary artery) away from the heart to the lungs.