I've got an RCBS handle that takes the 8-32 male threaded brushes which is fairly standard for US made cleaning rods - I've got adapters so that I can use them with my Parker Hale rods.
I try to avoid using greasy lubes in case it deactivates powder, in any case powder can stick to it if you don't clean it off. Graphite powder is better in that respect, you can buy it for lubricating locks, apparently mica powder works too...
I find that pulling expanders out of cases is tough without lube, but bearable if the necks are cleaned by ultrasound.