I've been working in the Entertainment industry for almost 20 years, and this is the first time I've ever heard of a permit being required for hanging theatrical lights. You'd be laughed out of the Permits office anywhere I can think of if you tried to request a permit for a light hang at a theater. There is NO WAY this is considered construction. Do I need a permit to build the scenery onstage?
Without knowing anything about where your friend is, this sounds like a small town where the inspector is unformed, board, and trying to justify his existence by bringing in permitting fees. Is he the only inspector, or is he the junior lackey? Have your friend go over the guy's head, if he can. This inspector is an idiot.
SceneryDriver
I'll eat some crow here. When I was a young, green, wet behind the ears city inspector I was home for lunch and watching the local news. Broadcast studio was across the street from my condo. They said "Pardon any noise you might hear; we're remodeling the studio". During our afternoon office hours I brought it up.
Chief sparky goes out there the next morning and met with the GC, came back and reported to us that it's only a broadcast television set being built and no permits are required for it.
Our statutes today exempt motion picture production sets and some other related things. Theaters are built with the expectation that things will be moved around daily and even during production; that's why there are house cranes, catwalks, etc.
To the OP:
I agree with Scenery Driver.
Inspector may need some education. It happens.