Lightning icing got its name because it goes on lightning cake.
This recipe appeared in the December 9, 1932 edition of the San Antonio Light. The explanation of the name, attributed to Mildred Kitchen:
Cake is one of the means of pleasing the whole family. The laborious manner of creaming one after another of the ingredients is a waste of time for a simple cake, where the ingredients involved are inexpensive.
There are a number of lightning cake recipes–the sort where all dry ingredients sifted together are combined with all liquid ingredients. I find myself coming over to their adoption, not to the exclusion of all others, but from now on I expect to use them rather frequently.
From a box sold in Canby, Oregon.
Chocolate Lightning Icing
2 cups powdered sugar
2 Tablespoons ground chocolate
3 Tablespoons hot coffee
2 Tablespoons melted butter
Mix ingredients in order given. Beat until smooth and spread cake. (Rich hot milk or cream may be used in place of coffee). If so flavor 1 teaspoon vanilla.