If you regulate the power to an LED, the power source shouldn't be much of a concern. Regulation can be as simple as a resistor, or as sophisticated as a dynamic boost/buck power supply that provides a particular voltage/current.
It's also possible to take advantage of known battery current characteristics and avoid regulation alltogether.
There are plenty of manufacturers and modders alike that overdrive luxeons with no form of regulation whatsoever. This requires careful thermal design, and comes at the price of emitter longevity and battery life. It's not the overdriving itself that kills LEDs - it's the heat that overdriving produces in a "stock" design.
