The current flow and high voltage spike from lightning would fry a capacitor.
You'd need one with a very low effective series resistance, a very high dielectric value, and a very high capacitance. Even then, assuming you could reliably get the lightning through the cap (the ESR would likely be higher than the ionized current path through the air, which would make the lightning go through the air instead of the cap), capacitors don't charge as quickly as all that, there's a time/charge curve that limits how fast it can charge.
It's remotely possible that we could store some small amount of the charge, but the usefulness would be limited, since we can't really get a strike to target effectively (even the rockets and wire don't get a hit all the time).
It could be set up to burn out flashlight bulbs, though
