If it does have any unique properties, we may be able to sort them out from the rf din of this galaxy. Your basic premise may of course be true. All we can say for sure is that we have not yet received them in a verifiable, repeatable, conclusive way. Analysis of the lightning spectrum has been done, extensively, by an electrical engineering professor named Paul Ryan. His work was done twenty years ago while developing a device called a Storm Scope, used by pilots to detect and avoid thunderstorms.
Lightning does indeed have a unique and unmistakable electromagnetic signature, at least on Earth.
Unfortunately, its energy peaks near a frequency of 50 kHz, a portion of the spectrum which will not penetrate our ionosphere. This is my personal opinion, which not everybody in the SETI community shares. For an alternative viewpoint, see this article . You do bring up an important point. One good way to verify that our equipment is doing what is expected of it is to use it to detect known natural electromagnetic phenomena.