Your set looks like this?
If so, it is a collet neck die and does not require lube.
I would take it apart, clean it thoroughly, buff out any obvious imperfections in the surfaces of the collet, buff the decapping/neck rod to a shine, lube the collet LIGHTLY and put it back together.
Use something like Flitz polish to polish to a shine and/or even a Scotch Brite pad to smooth the rough spots.
I polish the inside of mine by putting Flitz on a tight fitting bore brush and chucking the brush in a cordless drill.