I have never lubed the outside of necks regardless of the type of die being used…
I used to use graphite powder to dip the entire neck into when forming up or down using tapered buttons, but all it did was mess up the brass and die, stopped doing so pretty quick, there was no need for it, still isn't.
I've always used Hornady one shot according to most people I will get a stuck case, but it has never happened in several years that I've been using it. simply use it liberally and let it flash off before you put it up into the die.
I use all Redding Ti bushings. When I asked a Redding Tech if there was any reason to lube the case necks when using their Ti bushings, he said that they have found that lube will produce slightly more consistent results even though it isn't "needed". He recommended using Imperial Sizing Wax.
I roll my cases on a felt, lightly impregnated with 1:1 coconut oil / IPA mix. Wipe it off as I'm putting the case in the press. The body, shoulder and neck all have a film on them now. No build up if crud in the die and zero dented shoulders in probably a decade or more.
I don't understand why it wouldn't be beneficial, less friction always better when sizing brass. Just like the rest of the case being sized, very little is needed. I'm another fan of Imperial Wax. I bet I've had my can for +10 years and another 10 in there for sure.