I use White Lithium grease on the metal gears of my FW. Just a little bit and then spread it on the gears with my fingers. I know you said yours is a Kenmore, but I would think you could use the same type of grease on it that is used on the FW, without harm. You might google Desk Dave's at the Featherweight and I site and get a number and call him to inquire, since Billy is under the weather at this time.
Prayers and Blessings to you and family Billy!!!