I regret not taking pics of Lewisia cotyledon seedlings when I did their transplanting. The "stem" that these little guys make below the leaves and above the roots was already very thick. So if you can take close ups, have the camera ready; I think you'll be kicking yourself later if you don't. It was really difficult to transplant the roots in the soil media and at the same time keeping the neck in the gravel part. What I ended up doing is planting them on a little mound in the pot, and overlaying it with a thick layer of #2 grit and making a level surface. Not sure that would be the best way, but they did like it.
I haven't transplanted my Lewisia rediviva seedlings that came up last year. They retreated back into the soil relatively early. They don't naturally keep their leaves all summer, so I wonder if transplanting during the growth period is the right thing to do? Anyway, I didn't see an immediate need, so I left them.