Keep in mind oxytocin isn't effective after 48 hours post partum, unless the uterus is resensitized with estrogen. When the reproductive tract is under the influence of progesterone (all times except during heat cycles and around calving), oxy will only stimulate milk letdown, not cause uterine contractions.
Lute has two uses; regression of the CL (causes a cow to come into heat if she's currently cycling), and smooth muscle contractions. Smooth muscles include both the uterus, and to a certain extent, the lungs. (That's the reason for the warning label - shouldn't be handled by pregnant women or people with asthema.) So yes, Lute does help a cow to clean, because it will cause uterine contractions. I've used a series of Lute - 5mL every 12 hours for 2-3 days - with success on cows with retained placentas. When Lute doesn't work, oxy + ECP (estrogen) will usually do the trick.