You should not use a petroleum based lubricant. Here's a quote from the Winegard manual:
LUBRICATION (Done 3-4 times annually)
STEP 1: To lubricate the elevating gear, apply a liberal amount of silicone spray lubricant to the elevating gear with the lift in the down position. Run the lift up and down to distribute the lubricant over gears.
STEP 2: Two times yearly, or in the event rotating the antenna becomes difficult, normal operation can be restored by lubricating the bearing surface between the rotating gear housing and the base plate. Any silicone lubricant spray may be used. Elevate antenna and remove plastic plug from rotating gear housing as shown. Spray lubricant into hole and around edges of gear housing. Rotate gear housing until lubricant coats bearing surfaces and antenna rotates freely.
LUBRICATING RUBBER QUAD RING
Lubricate rubber quad ring on elevating shaft which is below worm gear with silicone spray lubricant at least twice yearly. This will keep quad ring from becoming brittle which could result in leaks down elevating shaft.