I'd imagine it is in fact possible to do exactly that, to store energy from lightning for later use. The problems come in the details, and if you can think of a good way to do it, you might get either rich or famous or at least do a small amount to help supply energy people like to use. That said, there may not be a whole lot of recoverable energy in lightning anyway, but it's worth at least speculating about.
Here are some of the problematical details:
1) Most places receive lightning very infrequently, but have a steady demand for electrical energy. The smaller the area you look at the fewer the lightning strikes will hit within that area per unit time. If you build some kind of device it has to be big enough to get hit by enough lightning strikes to supply the desired energy. If it gets hit once every ten years or so, you could be waiting a long time for a return on your investment. Bigger devices cost more.
2) Lightning has a high voltage but not a huge amount of current. Controlled sources of electrical energy typically want the other way around -- lots of current at lower voltages. 120VAC is what consumers can use, and they want a steady supply of it. Voltage and phase should not drift over time. Lightning can give you tens of thousands of volts over a few milliseconds and then be gone for the rest of the day. The lightning strike may damage the equipment, and still not have as much energy as we'd like to use. The problem is that the energy is deposited all at once, instead of spread out over time.
3) Much of the energy of the lightning discharge goes into heating up the air and making the glow. The available energy at the ground is just the amount of energy required to get the electrons into or off of the ground surface.
That said, there are some things you might do to harvest energy from atmospheric electricity that do not involve attracting lightning strikes. A tall lightning rod with a sharp tip will have a small current flowing from its tip, and a bigger one during a storm. There is a constant 100 Volts per meter electric field in the atmosphere which is maintained by the world's thunderstorms. Since air is a not-too-bad insulator when it's not undergoing electrical breakdown, it is hard to make a complete circuit from which you can extract energy. A conducting object (like a person, or a skyscraper) easily modifies the electric field in its vicinity.
(published on 10/22/2007)