I never used grease, as it attracts dirt , sand and other abrasive stuff. A dry lube like a graphite spray does a good job and is not messy or attracts dirt. proper Set up and sizing of a WDH hitch is more the issue. Lubeing will help with the creaks and groans, however as far as I know, wear from an un lubed hitch has not been a problem. They outlast both the tow and towed without noticeable wear.
All of my WDH hitches were basic Reese with right sized bars with chains to 'sturrup' type tensioners. some movement yes, little to wear. More complex hitches may demand more lube.
Think on this, a WDH hitch is a very slightly movably part that only is moving during hard turns. The purpose for it is to stabilize, equalize the weight between axles, thus reducung the effect of the Tail wagging the Dog.
To also reduce that effect, in comes the simple sway brake, or the old proven reese 'cam ' style sturrup bar end sturrup. Reese recommended in those old days to not use grease, as friction was a necessary part of the sway control.