I have Lee dies. When they are new they have metal shavings and factory dirt in them. I take then apart and wash in dish soap and hot water, and use a toothbrush to scrub them. Then dry all parts with shop rags. Then spray all parts liberally with gun oil or Ballistol and use fresh shop rags to wipe off the excess, then re-assemble.
I started out with Lee lube. but I stopped using it because of the dried lube build-up in the sizing die, especially around the shoulder. It required taking the die apart after every full length sizing session to clean up the solidified Lee lube.
For lube, I switched to using lanolin + 99% Isopropyl alcohol mixture pump sprayed into a plastic bag and shaken up, which lubes the entire case and inside the neck for the expander ball. Mix is 10 parts 99% alcohol to 1 part lanolin. Then place cases in a tray and either wait for the 99% alcohol to flash off, or speed the flash off with a heat gun which works in seconds. The lanolin mixture works very well for full length resizing, much much smoother than the Lee lube in my experience. However this method does require after full length sizing, washing the cases in hot water and dish soap to get off some of the lanolin, (but it does not all come off), and then tumbling in corn cob media to get the rest of the lanolin off.
The FL sizer dies still needs to be cleaned, but less often than the Lee lube in my experience.