It depends on many factors. The chance that lightning strikes an antenna a meter or two higher than your roof is almost the same as winning the lottery. The chance that lightning strikes an antenna 15 meter higher than your roof or the closest obstacle is more in the vicinity of you having a car accident the next time you drive to work.
Also, if lightning strikes your antenna protruding 2m, it will have struck your home regardless. Lightning can only ‘sense’ lower impedance paths from a meter or two, so if it comes so close to your home it will probably just strike something else on your roof.
If you really want to do lightning protection, it will set you back multiple times the cost of the gateway. You need a dedicated 16mm² copper grounding wire running on the outside of your house to earthing rods, you need a lightning arrester, … All this also won’t protect your gateway, just your house in case of a direct strike.
I still have to finish my lab story about lightning protection. I finished the text ages ago, but need to make some figures for it as well .