I use the Redding 38/357 profile crimp die. I tried it with & without lube it works best effortlessly when used withe Imperial sizing wax case lube.
I lube the first 5 cases then just lube every forth or fifth case or when the press handle effort increases. I tried Imperial Bio lube an hated it for every use I put it to because it so so hard to wipe off. The wax lube come off easy with a micro fibre cloth or paper towel sheet. When you see the unique shape that the profile crimp applies (looks like a tiny neck & shoulder of a bottle neck 308 rifle case) you'll see why lube is beneficial you will see no or little wear on the case brass. Less brass particles to Q-Tip out of the crimp die body. I think this type crimp works ok on lead bullets with the classic tapered crimp groove but it works best on jacked bullets with a cannelure. The amount the case neck is rolled inward is fixed by the dies internal dimensions but the length of the little neck that is formed is user adjustable from non existent to how much case you want to press into the die.