I don't like using any kind of oils on my snakes, natural or not. Personally, while cleaning the snake's cage with a 5% bleach - 95% water solution, taking care to wipe up all eggs that you cannot see, I let my snakes soak in a small container, Sterlite tub, with water that is neutral to our touch (aprox. 85 degrees) for about 30 minutes.
You can put half of a drop (very little) of diswashing liquid in the water to help break the tension between the mites' mouth and the snake. The mites will drown. You can also put a water bowl large enough for the snake to get into inside it's cage and let it soak itself. They usually will. Just change the water every day.
Clean the cage thoroughly again in about 10 days and soak the snake again. You can also soak it from time to time between cage cleanings. If you do everything right you should be rid of the mites within 3 cleanings.
Snake mites may temporarily suck on lizards but they generally don't host on them. You can use Equate Bedding Lice spray or Nix to spray the floor and surrounding racks, etc, as a safety barrier to keep the mites from spreading. Remove any/all animals before spraying near them, though. Once it dries you can put them back.
Best wishes!
HH
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Due to political correctness run amuck,
this ol' hillbilly is now referred to as an:
Appalachian American

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