ya, and the rechargables will handle a high current draw better, without a voltage drop.
so BASICALLY , the alkalines will start at 1.5V and as you hit them with a high current draw, will drop to about 1.2V then wane down to 1.0 and even .9 during a HIGH discharge rate. the NI-??? will hit at 1.4V hold that for a while, then drop to a 1.2V discharge rate, for the majority of thier existance.
then LITHIUM could be as high as 1.7V hit with 1.5V and actually stay there for a while, then eventually dropd down too.
if i would have FEAR of changing the batteries, it would be Rechargables HOT OFF THE CHARGER, or Lithium.
If any light cannot handle Heat dissipation in the long term, then alkalines would be better, because when the heat gets high to the LED, the alkalines will be weak by then and dropped in voltage.
that does not answer your first question, but to answer it, the best way would be to TEST with an ammeter on the tailcap, before putting it on (assuming you can) by putting an ammeter in BETWEEN the battery and the connection to the led, you could test for a short burst your actual current.
i would gladly overdrive a REAL luxIII 1.2 IF it has heat dissipation capacity, if it doesnt have great ways to remove the heat, then i wouldnt even run it at spec, let alone overdrive.
If its a REAL LUXIII its one hearty creature. if its one of them knockoffs, or doesnt have a way for the heat to leave, worry then.
then lower Vf , means that the LUX is more sensitive, also them higher output ones are oft lower Vf too, the lower the voltage that is required to drive the LED the more likely it will overdrive at some voltage.
Over time, the lower voltage LEDs tend to normalize anyways, so over time (burn-in) the voltage required to get to a specific current will be higher.
that does not mean that (over time) it is any more or less efficient (L/W), or will dissapate the heat of that any better.
it just means that more voltage will run less current through it after its broken in (or aged).
umm, so inconclusion. if the thing aint got no way to remove the heat, then dont put "better" current output batteries in it. because the alkalines will not put out the same current, over TIME.