L. lesliei on left and the one on the right looks like L. olivacea nebrownii.

I would just water them whenever they start wrinkling a little bit, you'll want a single, deep watering to make sure you get the entire root systems of your Lithops. Depending on where you grow them, a watering could be once a week to once a month. For the soil I just used a cactus mix from a nursery which people don't like here. I am positive there is a better soil medium to use than simple cactus mix, although I don't know what that is yet.

One more thing, I wouldn't dare plant them in anything but a pot unless you section off an entire non-connected space in your yard just for the Lithops, you don't get a lot of rain and you have a bigger plant in the same area that provides diffused light at all times of the day.

Got it! Thanks for your help, guys.

One more question: I'd like to get it out of that desiccated peat and into something grittier, but I don't think I can get the soil off the roots without wetting it/them. Should I wait to repot it until they're less plump, or will a short time under the faucet be okay? Should I even try to save all the roots or just let most of them grow back?

That's a tough one, I have had equal successes and failures doing it two ways. Sometimes I would wait until they were wrinkled as per usual, then repot them and give them a watering at that point in the new pot. Other times I would remove the soil from the roots, and plant them in new soil in a new pot and then give them a watering.

You could probably get away with planting them in the new soil right now in the new pot and leaving them unwatered to get the moisture from the new soil until they start to wrinkle up again.

It's getting close to Winter, when that hits you should probably refrain from watering them at all the whole season. Keep an eye on it though, sometimes they do need one or two waterings.

Thanks again.