Prepare a container for the repotted lithops. The container should be about 5 inches deep to accommodate the roots, but should be only slightly wider than the lithops' current container. Using a too-large container can cause the potting mixture to become stagnant.
Fill the container with a potting soil formulated for cactus. Alternatively, make your own potting mixture by combining 1 part coconut fiber, 1 part perlite, 1 part vermiculite, 4 parts coarse sand, 4 parts fine sand and 4 parts fine compost.
Remove the lithops from its container. Wear leather gloves to protect your hands from the spines that grow along the stem. Alternatively, create a strap from a strip of newspaper. Wrap the paper strap around the lithops, then lift the plant from the soil.
Place the lithops on top of the soil in the new container. Nestle the roots in the new soil, then jiggle the pot or tap the sides to settle the soil around the roots.
Place the repotted lithops in low sunlight two weeks. After that time, the plant will be established in the new container and can safely be moved into bright sunlight. Water the lithops lightly after the plant has been in its new pot for about a week.