The most likely thing is that the fine roots were damaged during transplant and rot spread to the taproot.

The best way to transplant Lithops is to remove all soil with flat spray hose attachment, carefully remove all fine, hair-like roots, allow plant to dry for 2-3 days in shade before potting.

The thing you realize after a while is that some of these plants just die sometimes. They don't all perform the same and the care can vary between species.

Also, you need to water them. At least give them a careful misting. They receive small amounts of water daily in nature.

Good luck!

Oh, and read this priceless info, linked below.

Here is a link that might be useful: It's Hammertime