The owners manual specifies Lubriplate or equivalent for the gears. Remove 4 screws and wiggle the cover off to access them. You will likely find most of the grease has traveled from the gears to the inside of the cover. So far, I've just moved it back into the teeth. When reinstalling the cover be sure the wires to the switch and light are positioned so the won't get pinched or caught up in the gears. The coupling between the head and the leadscrew needs a dab of high temp grease like you would use for wheel bearings. To get to the coupling, loosen but do not lose the 2 Allen screws that secure the head to the post then lift the head off. This is also where you would connect your hand crank if needed. If you don't rotate the leadscrew you can reinstall the head without having to sync the limit switches. There is no lubrication specified for the leadscrew and the manual specifically says not to pour oil into the tube.
Air Safe Hitch, Reese Dual Cam 800#, Centramatics