This is probably unrelated with respect to white lithium grease but I have been using it for black powder applications for the past 30-plus years.
I use it on the threads of the nipples and there is never any carbon build up. In addition, I have a Sharps paper-cartridge rifle.
In that rifle, I pack the cavity inside the gas check with white lithium grease and never have a problem removing it after I've shot it all day. In addition, that same gas check never fails to keep gas from escaping from the breech.
I also use the white lithium on the arbors of the colt-style revolvers and cylinder pins of the Remingtons. This always keeps the cylinders from binding due to carbon buildup.
Lately, I've read that some cap and ball shooters have been using white lithium grease to cover the balls in the chambers of the cap and ball revolvers. That wasn't without it's critics who were saying to never use it because you would never be able to get it out of the bore of the firearm.
I tried using it to place over the balls and didn't have any problems and it cleaned up without any problem. Now here's were my narrative will relate to one of the posts above that said the white lithium would be difficult to remove.
I don't clean my black powder guns with the traditional method of hot soapy water, which might be why some shooters can't get it off their guns. I use a solution of equal parts of, Murphy's Oil Soap, rubbing alcohol and hydrogen peroxide.
I use that solution just like a regular solvent for cleaning a firearm with smokeless powder. That's probably why I've never had any problem with removing traces of white lithium grease from my black powder guns.
I also dabbed a little white lithium grease on a piece of plastic the other night the wiped it clear with one swipe of my DIY black powder cleaning solution.
Now I'm not saying that there won't be traces of that grease left on metal surfaces on a molecular level, but from the naked eye and feel, I can't detect any greasy residue.
I use to use Moly Lube on all my actions but didn't like the black stuff getting on my skin and clothing and leaving a stain. For the past year, I've had excellent results using the Mil-Com grease, which is white and doesn't stain.