What kind of capacitor could build up, and maintain a charge acquired from lightning?
It IS possible to store high voltage energy, and probably possible to built a store that would not be destroyed by the first lightning strike. BUT even the biggest cap easily available will store less energy than a 2500 mAh NimH AA cell. Many such capacitors would allow significant energy to be stored "at a strike" but the store cost would be large. 

It would be possible to construct capacitors capable of say 10's of  kV rating which were protected [tm} by spark gaps so that the gap broke down well below capacitor destruction voltage. You would then potentially (pun noted) have a problem with back conduction of the capacitor via the ionisation path, but could very probably build a system that used a spark gap from input to capacitor to initialise charging and then another spark gap from input to ground such that it reduced the available potential of the charging spark gap and extinguished the arc. While this sounds rather "Heath Robinson" it is similar to the sort of things that are really done at extra high potentials. 

As an example of spark gaps being used as switches, a "Marx Generator" uses arc breakdown to cause spark gaps to act as switches and allow construction of a voltage multiplier witj DC input. Good trick if you can do it. You can ! :-)
 See "Marx generators below.



Capacitors:

You can make DIY multi kV capacitors aka "Leyden Jars - with glass jars or bottles - or even plastic "pop" bottles. From here 





Here's a 19 nF 10 kV cap made with foil and mylar shopping bags

You can buy capacitors in the nF range rated at 10's of kV.

Many offered here - Alibaba

Example from above - 40 kV, 10,000 pF disk ceramic.
 At 40 kV 10 nF will store 8 Joule.
About the same as a 0.64F cap at 5 Volt.  

Many very high voltage caps here - very worth looking at

1.3 uF at 100 kV !!!!!!!!!! :-)
 6500 Joule.
 Less than the energy in a 2500 mAh AA NimH cell (= about 10,000 J)





Marx Generators - as examples of spark gap switching.

This video of a 180 kV output Marx Generator operating is worthwhile just for the sound :-).

I am NOT suggesting that a Marx generator is what you need to meet your suggested requirement - but offering it as an example of how switching may be achieved by quite unusual but eminently practical means. 

Wikipedia - Marx Generator

The following is far from the most impressive spark-gap-switch unit image available - I chose it because it gives a good view of the spark gap switches working (small arcs  along the centre line) plus the resultant overall multiplied voltage arc (you should be able to find that without my guidance :-) ). To make this work you only need a voltage able to break down the small spark gaps. 



Worthwhile

LOPT in, 200 kV out](http://c4r0.elektroda.eu/_hv/index.php?page=hv/marx) Polish language.

Project with image



Very good project description.
"Quick &amp; Dirty" Marx generator





Karl would have been proud!