The black powder,from what I have read, burns at 2,000 degrees F. That's kinda hot. The tar from the burnt oil and the blackpowder fouling mix to form a hard fouling.
Inside the gun the fouling from the nipples gases goes right along the hammer and into the innards of the revolvers. The lube inside can take a beating getting mixed with hot fouling. Liberally coating the innards with gun grese or any grease works fine for me. When there'd enough grease the may turn it black but...it stays greasy and continues to lube the parts with it on them liberally. I put a clob of grease in the opening of the hammer recess exposes the parts inside to gas and fouling. That way the gas from the nipples pushes the grease in onto the parts and they are bathed in grease. Some comes out of the trigger hole in the trigger guard but I always carry a small rag to wipe if I need to.
I use grease on the arbors and base pins also and can get a hundred shots fired and sometimes up to 200 fired with out any real binding to sticky cylinders. I attribute that to the grease but more importantly the wax/lube in the lube pill(grease cookies) I place in the chamber right down on the powder. That has a splash forced down onto the arbor and the beginning of the cylinder center hole that just plainly guards the parts there from fouling causing the cylinder to get sticky. Most of the time I can get 200 shots off without having to use a drop or two of solvent on that area. I carry a Visine bottle with Old Slikum patch lube/cleaner with me and use that if need be to free up any thing.
Using the lube pills(one third lube like olive oil or mutton tallow or cooking oil of any kind and two thirds wax being bees or soy and paraffin) makes all the difference in the world. Using wool wads saturated with that recipie works well too. The lube just has to be 2/3rds wax so it's solid enough not to foul any powder.
The lube pills keep the chambers from the pill outward "clean". They also keep the barrels free from fouling accumulating enough to hurt the accuracy. I can fire 200 shots and not get a barrel fouled enough to harm accuracry when using the pills on the powder and under the balls.
Of course....the barrels and chambers are cleaned free of any storage protection that is petroleum based. Oil or grease has to be cleaned from the chambers and barrels. The barrel after cleaned ,from oil or grease from storage, by patches saturated with alcohol is then lubed with a patch that has "lube pill" squished into its fiber threads. Chambers too.
I guess the conclusion would be that petroleum can be used inside the gun where the moving parts are and the more in there the better and......no petroleum type oil or grease can be in the chambers or barrel when you fire the gun. Petroleum in the inside for the moving parts and natural lube for the barrel and chambers.
Lube pills are the best thing going to come to light for a cap&baller. They make it work much much better as long as the pill is "on the powder".
Make a melted stirred mix of the lube/wax and pour it in a rectangular cookie sheet and once it's solid again it can be punched out with a lube pill punch that has to "be made". Brass tube the right size to punch a pill is used. A short section of the right size for the pill is soldered into the next size bigger brass tube. They will fit together perfectly. The reason is that the short section sizes the pills when punched out and the long section you hold onto is a handle but more importantly lets the pills pass thru without sticking inside and getting squished as the tube fills with the pills. The pills come out the top in neat rows stuck together but...they slide side ways easily to separate them.
When pouring the wax/lube in a rectangular shallow cookie sheet to form a sheet of wax/lube to punch pills from the pan should be sparringly sprayed with "PAM" cooking stuff. Then......a sheet of wax paper stuck to the cookie sheet by the "Pam". The wax paper cut to size and pressed down into the cookie sheet should have the sides folded up the sides of the cookie sheet so wax/lube can't get under it. The reason for the wax paper is that the wax/lube sheet can be removed from the pan easily. It's not imperative since the pills can be punched from the cookie sheet itself but it's nice to make the sheets and place clean wax paper between and do the punching after all the sheets are made. The cookie sheet can be placed in a freezer for a few minutes after it's solidified enough and that expediates the solidifying. Freeze it too long and there can be cracks in the wax sheet.
The bras tubing can be cut with a small tube cutter from the hardware. The brass tubes come from the hardware store too. The pipe cutter makes a pressed in ring on the tube as it cuts and that folded in edge has to be filed off. Inside the soldered together sections of brass tube....the short section(half inch or a little longer) that punches and sizes soldered into the end of a longer brass tube the next size bigger and about 6-8 inches long....has to be assured that no solder is sticking inside the tubes restricting the movement of the "pills" up into the long section of brass tube. You want the "pills" to move thru the bras tube unrestricted.
The wax sheets should be thin. 1/8th inch thick and or even thicker if you want to use the "pills" as a filler to get the balls closer to the opening of the chamber(since the chambers are often tappered). I use the thinnest pills I can make which is about an 1/8th inch but some are bigger(it's almost impossible to level the cookie sheets perfectly so in the same sheet the pills are thinner on one side and thicker on the other. It doesn't make any difference though.
I use the thinnest pills on top the powder in my blackpowder cartridges so I like those thinner.
Anywhoooo.....there can be a little more to shooting a cap&baller than one may suspect if you want to go the extra mile and do it. You can get by with the most simple methods ,of course, which is petroleum lube inside on the moving parts and natural lube where the heat of ignition is with a natural lube over the chambers for safety or......you can optimize the function of the cap&ballers keeping them accurate with lube pills and reamed to the right size chambers and tuned actions with trigger jobs and aligned chambers to the bore and forcing cones the right angle and barrel muzzles concentric with the bore and sighted right to the point of aim ect.ect.ect. and all that too. One Pard I know called it ,"cap&ball heaven".
When his cap&baller functioned so well and was so accurate he was in heaven.