It is theoretically possible to store and harness the electricity from lightning, and several proposals have been advanced to show how this could be done. There are a number of reasons which make these proposals impractical, however. Lightning is simply not a good source of energy, and there are numerous alternatives which are safer, less energy-intensive, more effective, and readily available. In other words, just because humans can potentially and highly theoretically store electricity from lightning doesn't mean that they should.
On the surface, lightning seems to have a lot of potential as an energy source. It is totally renewable, which is a definite advantage, and it is readily available in some regions of the world. Furthermore, lightning has a lot of energy; a single bolt can power 150 million light bulbs. The idea of harnessing so much energy and storing it is immensely appealing.
There are a number of problems with trying to harness the tremendous energy of lightning bolts. The first is that lightning is highly unpredictable. There is no way to know exactly where and when lightning will strike, so it would be difficult to find a location to turn into a facility for processing lightning for energy. Lightning also delivers its energy all at once, which would require huge batteries and capacitors. Otherwise, the energy would simply blow out any systems established to capture it.
The potential instability in the supply of electricity from lightning is far less of an issue than the infrastructure which would be needed to support the energy collection process. Lightning is so powerful that it would overload all but the most sophisticated and heavy-duty systems, and the wisdom of building and installing such a system would be questionable if it could only harvest the energy from a few lightning bolts a year. Even in areas where lightning is frequent, the cost of the system would probably outweigh the benefit of getting electricity from lightning.
Humans may at some point develop a system which can cheaply and effectively collect and store electricity from lightning. Technological innovation is a natural part of human societies, and advances are constantly being made. 18th century humans would have been astounded by the things developed in the 19th century, for example. Such a development is likely to occur in the distant future, however, making it more important to focus on accessible sources of alternative energy like sunlight, wind, and water.