Unfortunately you can't put a set time because its not like the laser works for x minutes and then stops. The output slowly drops off until it starts flickering, or mode changing, or something else to let you know you're out of juice.
With an x-105 the pump diode is ~500mW, so lets just assume power input is somewhere ~1.5-2W between inefficiency in the diode and driver. That means your current draw on 2xAAAs will be ~500-667mA (this figure is pretty accurate in practice actually). You can use those numbers with the spec sheet to get an idea of how long you have before the laser can't lase anymore.
I think we are missing one piece of the puzzle to find the answer....
The laser will stop Lasing at a value greater than ZERO.....so while there is still power remaining in the cells...for all essential purposes it's dead.
it would depend on the voltage threshold of the diode, BUT lithiums hold their voltage right up until they go flat for the most part. so if you have 2 AAA lithiums with a combined capacity of 2400mah and you draw say 700 ma/h on a load. assuming you get 85% you should get ~3.5 hours
the threhold though is considerably lower though so you should actually get closer to 95% before they go low enough to start suffering a voltage drop serious enough to stop lasing.
Ashton,
The voltage of a single lithium ion battery fresh off the charger is 4.2 volts. From there the voltage will drop quickly to appx. 3.7 volts, and then slowly drop from there.
Anyone doing this with any type of non-rechargable batteries is waiting for a terrible accident to happen, especially with lithiums...don't do it!
Get some decent AAA NIMH batteries. I am using eneloops in my X105 and they are holding up very well. I just got back from the store and bought a pack of E2 AAA lithiums to try in it. I will be reporting back a little later.