I don't have an answer for you on what the best battery pack will be for your application, but I can tell you lion cells can easily come off the charger at 4.2V, hence your 8 cell pack could charge to 33.6V or possibly even a little higher depending on your charger. Granted, voltage may sag some under load, but I wouldn't risk it.
I would possibly recomend AW C cell, but they are currently out of stock. 2 in series should meet your requirements.
http://www.cpfmarketplace.com/mp/showthread.php?t=169872
The kaidomain D size li-on (32600) on paper should also do it, but I recomend you search around here for discussion on it first. I know there has been some concerns with quality of the protection circuit.
I would think 2 cells would be enough, I suppose you could always add a third.
From what I see on the luxdrive data sheet, you need only to keep your voltage at 2V over your led VF, and at 1A on a parallel wired MCE that should be relatively low. (3.2V maybe??)
But I don't see why you need 3 buckpucks to do this? Couldn't you do the 3 MCE in series with one driver and 3 or 4 cells? Or am I misunderstanding your sketch and you aren't wiring the dies in parallel?
If that's the case, forget everything I just said
Oh, PS don't solder directly to Li-ion cells, that would be bad, and I suggest you get batteries with a built in protection circuit. I don't think the lux drive drivers have any sort of low voltage cut off and you don't want to run those cells too low. NIMH could possibly be a better alternative, I will let the experts weigh in.