Gun Scrubber works well. So does plain ole' rubbing alcohol. I do not lube carbide pistol dies but do spray the interior of bottle neck rifle dies with the spray case lube I am using at the time (per the lube manufacturer's instructions).
I use "Simple Green" to clean dies and guns. It is a wonderful cleaner and degreaser. Disassemble the dies or gun, pour SG into a pan on em' paintbrush/partsbrush to swab at em', bore brush and/or toothbrush for details, soak some more, rinse in hot water, towel dry then air dry for a while, then spray, swab, flood with breakfree CLP, let "cure" for awhile, then clean cotton rag and q-tips to remove all oil possible, reassemble. SG cuts lead, copper, lube, wax, grease, everything. Its great!
"Always place your clothes and weapons where you can find them in the dark"
Spray them down with WD-40(or equivalent) and blast with high-pressure air. No residue. Clean as a whistle. This method works great for trigger assemblies and any areas hard to get to. Dirt is your enemy, clean is your friend.