What is the minimum height a building should be before a lightning protection system is installed ?


depends on it’s surroundings. A small shack on a mountain top will need protection.

found this:
A risk assessment guide for determining lightning loss for all types of structures can be found in Appendix I of the National Fire Protection Association’s lightning protection Code, NFPA 780. This guide takes into consideration the type of structure, type of construction, structure location, topography, occupancy, contents and lightning frequency.

but this code doesn’t seem to be available online.