In using Lee's push-through sizing kits, some lubrication of the boolits is important. Dry boolits can be too hard to push through with a standard press unless you back the die out so it moves the boolits just a little as it cams over. Learned that trick the hard way after sticking boolits and trying to hammer them through to get them out, which ruins the boolit and beats up the plunger.
Lee intended that we'd lube them with LLA, push them through the die and then relube them with LLA. That's messy, if you're applying gas checks it gets lube under the check, and if you're going to heat treat the boolits after sizing you will incur the wrath of your wife for stinking up the oven. Any sort of petroleum based lube such as WD-40 and the like will have similar objections. I tried PAM cooking spray so it wouldn't stink in the oven. Worked well, but it smoked and left a brown varnish on the boolits after baking them.
Then, slow as I am, I realized why the boolits are so much easier to size right after they're water dropped than after hardening up for a few hours: It's not just that they're softer. They're WET! Dip the boolits in water right before sizing, and they go through far more easily. There's no residue left on the boolit, and no stench when they're oven-treated.
I then tried putting just a little bit of Murphy's Oil Soap in the water, and the boolits really went through the die easily. I gave 'em a quick perfunctory rinse before heating them, and there was no stench. Just a little residue in the form of a white powdery deposit on the boolits from soap I didn't completely rinse off. Interestingly, the gilding metal Hornady checks came out yellow brass colored after soaping, roasting and quenching.
Those of you with background in metal fabrication will find this old news. Soapy water's been used as a metal drawing lubricant for eons. Cartridge cases and primer cups are made with soap as the drawing lube. (Bet it works for a case sizing lube, too.)
But plain water works quite well for boolit sizing. Try it, you'll like it.