Lithops are captivating weird plants that many people love. They are easy to raise from seed but harder to keep alive once they reach adulthood.
Here are some guidelines for long term sucess based on our experience:
Soil: Unlike Haworthia, Lithops won't do well planted in pure pumice. They have fine roots that need to grow into a more fine substrate. I have had luck planting them in a gravely soil mix that is roughly 2 parts decomposed granite, 1 part loam soil, 1 part gravel (builders sand), and 1 part pumice. A mix of 2:1 mix of pumice and coir (coconut based soil) works as well. Avoid soils overly rich in organic matter and peat.
Watering needs: Water them infrequently but give them a good deep soaking once in while to encourage the roots to fill the pot.
Learn about the lithops life cycle:
Light: Give them lots of sun but protecting them from hot sun during the spring and summer. Morning direct sun is good. If the temperature gets above 90 put them in shade. Lithops will become etiolated and rot prone if they don't have sufficient light.
Transplanting: Trim back the roots a good deal while transplanting. The roots will develop a thick corky covering. Scraping away a small bit of this corky layer (I use my nails) to reveal the white inner root will help stimulate root growth. Water after transplanting (no need to wait for the roots to heal) to encourage root growth.
Keep them away from squirrels.