First I will discuss a spit or water-lubed patch. The patch in back of the ball is exposed to the flame and is heated by convection and radiation. The layer of water nearest the flame will vaporize. So the very back surface of the patch is full of steam, the rest of the patch is still soaked in water. Steam is a poor conductor so the convection of heat into the patch almost stops at this thin layer of steam. Radiation from the flame will penetrate the layer of steam somewhat. As the patch travels down the bore the layer of patch that is filled with steam gets thicker and the layer of patch that is soaked with water gets thinner as the water vaporizes. One (desperate)way to escape a burning building is to wrap yourself in a wet blanket - but you'd best get out before it dries, and it will dry quickly! The thin area around the ball where the patch squeezes into the lands/groves is another story. If there is much leakage then the hot gas will race through the gap at a few hundred miles per hour. This will dry the patch out fast and cut it as well. Racing hot gas will cut things in short order, and is how the first space shuttle disaster started, with a small leak of hot gas around an o-ring. This is why the right combination of patch and ball will help eliminate cutting and burning.
So if the patch is tight enough only the back half "sees" much hot gas, and if there is enough water for the short trip down the barrel the patch never "runs dry".
Oils are different than water. They are a mixture of light and heavy hyrocarbons. They do not have a fixed boiling point like water. At certain temperatures the lighter hydrocarbons boil off, then at higher temperatures the next lightest ones boil of, etc. So with a pure oil lube the various hydrocarbons are boiling all along the barrel. Some of the heavy ones can form "coke" or "sludge", a thick crud, but at high enough temperatures even that burns off. It would be impossible to analyze exactly what a given oil would do in the short violent trip down the barrel, you would need tests and pictures and temperature measurements. (Trust me I have tried to predict temperatures in various industrial devices for many years, including boiling hydrocarbons in long tubes).
A mixture of oil and water? Even harder to predict!
Moose snot? Forget even wondering about it, just try it and see if it works for you!
I suspect the best mixtures loose oil/grease from the patch in a way that deposits them mostly on the barrel, and the worst mixtures loose the oil and grease in a manner that is conducive to them burning or solidifying in a hard crud.
Another idea that I had is that the high pressure behind the ball might actually force the liquids forward through the patch between the ball and rifling. Imagine a lubed ball stationary in the barrel. If you blew (hard) from behind the pressure might make the oils/water wick through the patch and out the othe side. So maybe the patch acts as a wick and allows the vaporized grease and water to replenish the thin layer between the ball and the barrel.
This is truly an area where an enlightened experimenter can be generations ahead of a scientific analyzer.