With all my black powder firearms, with the internals, if a part is designed to slide, it gets grease. If it rotates, it gets oil.
A long time ago, I was taught to use boiling water to clean the barrel. No reason was given. Now, water temp at about body temp works well, along with a bit of grease/oil cutting detergent. If I've been in a dusty environment, I also clean the internals, otherwise that part is a job done twice a year. And those parts don't seem to object to either natural or synthetic oil or grease. At least I've seen no picket signs parading around the house.
A long time ago, I was taught to use boiling water to clean the barrel. No reason was given. Now, water temp at about body temp works well, along with a bit of grease/oil cutting detergent. If I've been in a dusty environment, I also clean the internals, otherwise that part is a job done twice a year. And those parts don't seem to object to either natural or synthetic oil or grease. At least I've seen no picket signs parading around the house.