There's several teams of scientists and electrical engineers, etc, out there working on this idea right now, but as explainined in a course I took on energy conversion it's a bit of a pipe dream.
The trouble as I understand it is not so much the storage, it's that the majority of the energy is dissipated as light, sound, and heat. What's left over in a typical bolt of lightning is only enough to keep a 100W bulb lit for about a year.
Secondly, the fact that lightning exists as a huge surge of current lasting only a few brief seconds or milliseconds means that for the majority of the collection systems life, it will not see any use. And because not every bolt of lightning is the same, the collection systems will have to be built with a huge safety factor... What happens if you get happen to get a freak bolt larger than the system is built for? You damage the collection system and take out power (or reserve power) to consumers. Also, accurately predicting the availability of power and adjusting the price per kwh accordingly is impossible since summer electrical storms are not guaranteed to strike regularly and are not always the same strength.
There's also the social factor. You'd need to build a helluva huge lightning rod to have even a chance at collecting on a regular basis. People aren't gonna want to live anywhere near that thing, not just because it's a big ugly stick, but because it's gonna be loud and dangerous as hell if it works.
There's no problem with creating batteries capable of storing the energy, the problem is getting the power to the batteries in the first place.
edit: I just read my response again and it feels like I just skirted the issue but didnt answer the question related to practicality.
I think there's no question that it'd be possible to capture lighting energy if you built a collector on a grand enough scale that it could stand up to the surge and temperature of the blast - but it would not be socially or economically beneficial to do so. Depending on location, you might never break even on your initial investment when maintenance costs are figured in.
I had a brainwave... if there were a reliable way to trigger lighting strikes from the ground as a storm passed over, the lightning rod could also be used as a thermal reservoir for thermoelectric cells or to heat (or reheat) water for a nearby cogeneration plant. In that case you've eliminated some of the losses due to heat dissipation provided the cells dont melt or short during the strike. I'd be more than a little nervous about the cogeneration idea though... lightning heated water..... could be a bad mix.