My understanding is that Perlin noise is designed so all of its patterns are close to one single "size", but lightning is a fractal with patterns at every "size".
There may be a way to use several Perlin noise systems at different scales to make lightning, but perhaps one of these other methods would work better:
The midpoint displacement method is a very fast algorithm
for generating shapes that look a lot like lightning.
Alas, it only generates a (very jagged) lines between two points, never forks.
There's some source code and pictures at
http://www.krazydad.com/bestiary/bestiary_lightning.html
Probabilistic L-systems can be used to generate shapes that look like lightning.
I see that at least one person abandoned Perlin noise and switched to L-systems in order to simulate lightning.
http://www.grepart.com/showcase/content/lightning_paper.pdf
The stochastic Lichtenberg algorithm runs somewhat slower,
but it is more physically realistic model of lightning and generates lots of forks.
http://fisica.ciencias.uchile.cl/alejo/fractal_antenna/node7.html
Is this a dup of the "Best lightning generation\simulation algorithm?" question?