In a rifle case the neck is sized down as it goes into the sizing die .
Because neck walls can vary in thickness and thus leave inside necks of varying diameters
... the expander ball on the mandrel is used to insure every case neck is the correct inside diameter ... when the ball is pulled back through the neck , that is when the neck gets it correct size and every case has the same inside diameter .
Of course if lube on the outside makes sizing a case easier ... then lube on the inside of the case neck will make pulling that ball back through the undersized neck easier also !
Any lube will do ... it makes pulling the ball out easier and it will cut down on case trimming ... Some reloaders swear that a case gets longer when you don't lube the inside of the neck ... the ball pulls the neck out just a little ...stretching it !
I find lube in the case neck does make re-sizing easier .
Most people like to use some type of dry lube , greasy lubes stick to powder ...
I like to use Lee Case Sizing Lube , white stuff in tube it's a water soluble Wax type lube , applied a thin film with a damp Q-Tip to the inside of the neck ... it dries to a dry lube filn in 30 seconds and it doesn't have to be removed , not greasy , not messy and it's dry , doesn't stain hands black like some stuff ...
... It's As Good as Any and Better Than Most !
Do use some type lube ... it does help .
Also polish mandrels and balls where they contact the case ... a super high polish job with polishing compound also helps big time !
Good Luck ,
Gary