Can Lagerstroemia indica seedlings live in lime?

This depends on how to do it. Planting trees with stones and ashes requires not only strength but also brains.

Lime pile is short of water, the most important thing is the lack of soil. Many lime piles are bare, or there are only a lot of gravel. It is difficult for seedlings to survive in stone piles, so soil must be cultivated for them.

The survival of saplings needs water, photosynthesis and necessary nutrients.

If you take good care of the soil in the later stage and don't let the rain wash away, survival is not a problem.