This is one sketch I made, originally including an idea for marking when other events occurred (in the sketch, a tornado).
Here are some screenshots I took in the development process, which included troubleshooting the spherical coordinate system, and correctly mapping states to the surface. Originally the data was plotted as floating points, but that was later changed to the height-map.
I am very happy with the final results, which show the lightning data from 2012. I experimented with coloring the height map based on the underlying state, but I think coloring the triangles by their average altitude looks better.