If it's anything like a "Zeus" that gets put on the breaker box feed...
A Zeus is a dual gas discharge tube that goes across leg A and leg B of your power line, to common.
If surge or spike greater than about 400 volts comes down either leg of the the power line the gas tube lights, discharging the surge. It is a surge/spike protector. Because the Zeus triggers at 400V you still need a smaller ones at the computer/electronics devices. NOTHING will protect your house from a direct lightning strike on your power feed. Absolutely nothing! Lightning hitting a tree will blow the tree apart - from the expansion of the steam created when the moisture in the tree boils, in an instant.

I was talking to the guy that installed one in my house in Florida, about lightning and the Zeus. (We had a master feed box outside, where the Zeus was installed.) He state that he did replace one on a house that got hit by lightning,... he found little pieces of the Zeus all over the yard. I don't remember what he said about what happened to the rest of the house though. Lightning hitting a tree will blow the tree apart - from the expansion of the steam created when the moisture in the tree boils, in an instant.

One time a lightning spike came down the phone line, lost a phone and a modem on that one (heard the characteristic SNAP). Once down the TV cable, lost the cable box and a VCR on that one.

It's more protection than nothing, but not a savior.

Yep, there is a huge amount of energy in a lightning strike. In fact, many hams and commercial installations thermite weld the ground wire or braid to the grounding rod to prevent any resistance (a lightning hit would melt solder).

I have had two near hits by lightning - one on a sailboat, and one in the transmitting “shack” of a UHF TV station. When you feel the hair start to stand up on your body, you are very near possible death! Current thinking that I’m aware of is the best strategy is not to lie down but Instead squat down making the lowest possible profile with your feet together. If you lie on the ground the potential difference in the earth from one end of your body to the other can be enough to kill you. Texas has the most lightning strikes (maybe because it is so large?), but Florida is high up on the list.

The potential difference and equalization can happen anywhere hence there is air to air lighting and also the spark from the fingers to stuff we touch. From what i know, Air-Ground strikes are more studied but Air-Air events happens more frequently.

As for the lightning going from ground to air, that is the actual electron flow. Electrons travel from the negative to the positive. We are just accustomed to the positive to negative idea and is still taught as the conventional current flow. Hence the term "discharge" aforementioned refers to the current flow which is positive to negative.

Lightning is a complex process and the actual flowing of electrons happens near the end of the process. Before electricity can flow, it first has to have something to flow on. They call that a leader. The leader can go either or both directions into or opposite each other to produce the conductive path. - ground to air, air to ground, air to air etc.

Lightning rods are designed to help discharge any static potential buildup, not attract lightning.
But if it were to be hit, the cabling to ground will hopefully conduct any static discharge, thus saving the building, statue, or whatever they are installed to protect. If they were designed to attract lightning, most everything that has them would get hit.

Static charges bleed off pointed objects much faster than round objects (like the top ball on a Van de Graaff generator that is designed to save a static charge.)

https://physics.stackexchange.com/questions/65825/does-a-lightning-rod-prevent-lightning-strikes