One of the easiest ways to animate lightning is to create the lightning bolt ahead of time. You can draw the lightning bolt by hand with light colored pencils on a black sheet of paper or you can create the lightning bolt digitally using a program such as Photoshop.
Creating lightning digitally has certain advantages. The airbrush effects in digital programs can be used to create ambient light around the arcs of the bolt itself. There is also little clean up or switching of tools, and this cuts down on the overall time for the project. Regardless of which method you choose, start by drawing out a white line that breaks apart into several smaller branches. These resemble the roots of a tree. You can then use an airbrush or digital airbrush tool to create a soft glow around each arc and branch of the lightning.
Once you have completed the drawing of the lightning, you can begin to animate the actual strike. You can do this in a few different ways. If you are using more traditional tools, simply lay a sheet of black paper over the lightning bolt. To create the illusion of the lightning striking, slowly move the black sheet down the length of the bolt. This will reveal more of the lightning in each frame.
If you are creating the lightning strike digitally, duplicate your lightning layer four times. Change the opacity of each layer so that the top layer is faint and the bottom layers become increasingly opaque. Erase much of the lightning on the top layer and erase less and less as you go down the layers. This will allow you to create several frames where the lightning appears small and faint and then grows and becomes brighter. Save each layer as a separate image to create the frames.
Every lightning strike should be punctuated with a dramatic conclusion. One way to do this is to add the characteristic flash of white at the end of the lightning strike. This can be done by creating a few frames where the lightning whites out the surrounding clouds and sky. Simply paint light strokes of white around the general area of the lightning bolt and expand this white mass in each frame. If there is a character present, you can cast some white light on their features to show the light spilling across objects.