Grease type help?

I really wish I could post this in watchmaking as I wonder what the oil experts would say about viscosity etc.

Anyway, I picked up a broken used automatic litter box for my cat and as I've done with watches I wanted to tear it down and fix it. Just needed some connections cleaned. Cat owners apparently aren't as hands on as watch people. Can anyone recommend a good grease to lubricate the small gearbox? The motor is of unknown specs probably trying to keep their plans a secret. It's a dc type motor. I suspect high torque low rpm as the globe itself moves very slowly.

Gears are a mix of plastic(?) And metal gears.

Any reccomendations are appreciated. Thanks!