Years ago I “discovered” lubing the inside of the case necks goes a long ways towards making necks straighter on every type of sizing die I’ve tried—this includes the LCD’s
I keep 5-6 tins of imperial wax in the fridge. I dip the necks into the stiff wax (the cold wax makes the whole process less messy and easier to control the amount applied), and lube the body of the case when using the wildly popular PFLR method.
I have tested the Imperial dry vs Imperial wax using the same lot of brass and same die more than once. Necks were straighter (sometimes only slightly straighter), and less stretch (sometimes quite a bit less stretch) when using the wax.
I’ve also tested other lubes from the original RCBS gooey sticky stuff to spray on lube. The wax made straighter necks with less effort on the press handle. The only exception was the STP oil additive that I tried, it worked very well—but Imperial wax was a lot easier to deal with.
Maybe I’m being anal, but I don’t want ANY residual lube in my chamber. After sizing I drop the lubed brass into a small parts bucket of lacquer thinner. When I’m done sizing I pull the basket out, swipe a neck brush into the necks and blow them out with compressed air.
As I mentioned. I have started dipping the necks in the dry lube to help prevent bullet weld.