What he said. I've tried running a KX2 on an 18650 cell. I'm not entirely satisfied with the performance. Even the large li-ion cells don't hold the voltage high enough to run in regulation for as long as I would like. It seems like a waste of the capacity of the cell.
It does run for a long time (on an 18650) but the output is dropping for a lot of the run. I'd just as soon run it direct drive, or maybe with some kind of LDO circuit.