I have yet to find (with one exception) any device which can take alkaline AA batteries but not lithium AAs. They are pretty much the same voltage after all. Ditto for AAAs.
The one exception was ages ago: a Petzl headlight with an incandescent bulb. It was over-driven by the alkaline batteries, surviving by grace of the internal resistance of the alkaline batteries. When you used lithiums the internal resistance was much lower, and the bulb blew. But that was a silly design in a previous era.
Actually, white LEDs are very tolerant of small voltage deviations, and the CREE LED used is not driven at full rated power anyhow. To use that CREE LED at its full rated current you would need to heat sink it!
Cheers