If you manage to make some huge capacitor on the ground and connect to an lightning arrester on top of a say 300 m isolated antenna tower, the capacitor will sooner or later charge to the potential of the air at 300 m (assuming lower leakage in the capacitor and feed line than through the surrounding air). The lightning arrestor tip potential would finally be about the same potential as the surrounding air at
300 m, thus, reducing the likelihood to that electrode, compared to grounded 300 m arrestor. Thus you may have to wait for the hit quite a long time.If the lightning hits after all and the capacitor is charged, but there is some flash over between the plates (perhaps only weak point), the arc will burn as long as there is sufficient power to maintain the ionization in the arc. With a large capacitor with a large charge, there is going to be a large current maintaining the arc, hence dropping the voltage across the plates.
When the voltage has dropped sufficiently, the current is no longer capable of maintaining the arc and it will blow out. However, the remaining capacitor voltage is now much less than the initial flash over voltage, so very little energy can be recovered (energy proportional to the square of capacitor voltage).
Why wait for the lightning strike ? There is a quite a steep (20-200 kV/m) voltage gradient in the air during a thunderstorm that could be utilized. Benjamin Franklin essentially tried this. Using a balloon, lift a string of series connected capacitors into the cloud and let those capacitors be charged.
To collect enough charge, 2-3 balloons may be needed to suspend a "collector" net between them. When the capacitors have been charged, disconnect the "collector" from the capacitors and lower the balloons.
On the other hand, if there are high towers, in which the lightning arrestor is frequently hit, why not put a current transformer at the lower end of the grounded arrestor to capture some of the energy ?