To lube or not to lube the hitch ball

Before each trip, I put some white lithium grease on the top of the ball, but not around the sides or bottom portion of the ball. When not towing, I cover with the plastic cover.

I can't imagine what temperature the ball generates with all that pressure and no lubrication.

I think the main reason people say do not grease, is for fear of the hitch sliding off the ball during towing.