FWIW: I've found lubing the Lee Turret Spiral Press index to be the biggest mess on the press.
I started trying a "different type of lube" and found it works very well and little or no mess.
. A trick learned driving wood screws into hardwoods is to use CHAPSTiCK to lightly lube the threads.
I tried the CHAPSTiCK on the Lee index rod and the plastic square works perfectly. I just dab a small bit in each rod groove above and below the ratchet. It works very well and leaves no oily/greasy mess.
For the few that use the Lee Turret Press, give this a try using the "original" basic CHAPSTICK. I think you'll like it.