Your question potentially touches on several different questions and issues...
In most states as far as I know, any kind of stamp purporting to 'engineering' must be done by a licensed engineer. Otherwise it would be considered fraudulent and a violation of the relevant professional laws regarding engineering.
That said, I'm not aware that most states require lightning protection systems to designed by and engineer or other qualified individual. Indeed, lighting protection is generally optional and not required by building codes as far as I know. There are a couple codes to guide the design of LPSs (one is NFPA 780), but unlike other codes that states typically adopt into law in some form, I'm not aware of any states that adopt an LPS into legal code. So it is possible that in your state anyone can design an LPS because they aren't really subject to regulation.
I've also heard tell of a UL certification for LPSs, and I'm not sure how that relates. There are probably other non-government entities issuing credentials in lightning protection training.
Regardless, the 'who is legally' part of your question will be answered by looking to licensing or permitting law in the relevant state, and not to any nationally or internationally developed building code.