The problem pointed out in the thread about the LED Lenser V2 3xAAA was that it was pushing 1000mA through a LuxI. That is not good for the poor LuxI's health (recommended forward current is 350mA).
A LuxIII is designed to run at 700mA, but according to Lumileds' data sheet, it should be able to handle 1000mA (although that's the maximum recommended forward current). The initial measured current of 1800mA mentioned in the V2 thread is definitely not good, although the poster implied that he was using NiMH batteries hot off the charger (1.4V).
http://www.lumileds.com/pdfs/DS45.PDF
How well the light manages heat is another issue, which is unknown.
I'm not saying it's a good idea to overdrive a LuxIII like that. I'm just commenting that it should be able to handle that level of current better than the LuxI light mentioned in the linked thread. Some users might not mind potentially reducing the lifespan of the emitter, as long as they get 80 lumens by overdriving it. For $26.50, why not?