Specifically, I've got a line on some AA size 3.6 volt batteries. My guess is you'd get a quick flash and smoke, but what have some people done with those batteries?
There called the 14500 I put them in xnova 8led and ghostll lights it sure does make a difference in brightness been using them for more than a year now still super bright.
L1p with 3 volts = pushing it. 3.6 volts (or 4.2 volt hot off charger) = very bright and hot for 20-40 seconds then darkness. The circuit board cannot take the voltage and frys. The lux will be fine but no more light until you replace the board.