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This can mean a few different things. They do this when they need water, but they also do this when they are dying off.

Part of their natural process will be to put out replacement pups that you can't see until they emerge from under the original plant. They do this as they are dying off.

Yours don't look quite mature enough to be dying, so I would chalk it up to needing water. Give it a good soaking, then let all extra water drain out completely.

This article will help you to care for these plants: https://www.gardeningknowhow.com/ornamental/cacti-succulents/lithop/growing-living-stone-plants.htm

You are right. The new "leaves" grow as the old leaves wither away. Ideally, you leave the old leaves on, they eventually turn to a papery sheath. All you can do is provide optimal care. Here are the growing conditions:
https://wimastergardener.org/article/living-stones-lithops/

https://www.gardeningknowhow.com/ornamental/cacti-succulents/lithop/growing-living-stone-plants.htm

The best practice is to let the plants tell you when to water. They will start to shrivel when they need it. The time between waterings will depend on the environment, so waiting for some shrivel will cut out all doubt.

Here is an article that will help you to care for the plant:

https://www.gardeningknowhow.com/ornamental/cacti-succulents/lithop/growing-living-stone-plants.htm

I would not disturb them. They are going to be very slow growers. You can feed them, however, when you resume watering. Just be sure to mimic their native environment as much as you can.

https://www.gardeningknowhow.com/ornamental/cacti-succulents/lithop/growing-living-stone-plants.htm