Although the topic of lightning can be an entire masters or doctorates program, when doing my roof antenna this is what I found. It can likely apply to lightning rods as well.
The reason a roof antenna has to be grounded (an attic antenna does not) is because wind blowing over it builds up static electricity which attracts lightning. I can't say if wind blowing over your roof, gutters, or lightning rods will cause static buildup. By grounding it, as the antenna builds up static electricity by wind it's harmlessly directed to ground decreasing the chance that your antenna will be chosen to be struck vs. say that oak or elm across the way that's not disappating the static electricity as well.
A roof antenna has to be bonded to the breaker panel so everything has the same (I keep forgetting the word... charge or something you want the antenna having the same charge as everything else in the house so you don't shock yourself). That does 2 things, prevents shock and the antenna's grounding rod needs moist dirt. If it's been dry for a long period of time the grounding rod may not be able to release the build-up of static electricity so by bonding it to the breaker panel that eliminates that issue. Though, the code behind why you have to bond an antenna's grounding rod to the breaker panel I'm pretty certain has nothing to do with lightning or dry dirt, it is a good thing.
The next aspect of grounding the roof antenna is that it should be (it may be code) grounded to a grounding rod directly below with minimal bends & curves. This has to do with if the antenna gets struck. All bets are off at this point, the only thing you can do is attempt to direct the strike where you want it to go instead of having it decide to take a shortcut through your house or something. It is certain with lighting rods and properly grounded antenna getting struck is going to cause massive damage BUT the goal is to attempt to direct it to ground ASAP so the damage is not catastrophic or with casualties. Since lightning doesn't take corners very well any bends of the grounding wire to the grounding rod should or must have a large radius, and should be as straight with little bends as possible to the ground rod, but expect serious damage. Not all the lightning is going to choose that path and even the smallest fraction that doesn't will cause massive damage.
Okay, you're probably bored. Things to think about, are your lightning rods connected in as straight a line as possible to grounding rods burried below? Are they connected to the breaker panel? Is your soil/dirt dry?
This doesn't discuss lightning feelers... and all I know about is a small bit of why a roof antenna has to be grounded and how best to do it... I really don't know about lightning rods but perhaps some light was shed. Lightning is so vast this hardly scratches the surface.