Ill have to look into that myself.
I ran the little eos test last night/today, 15 hrs on the 20lumen level with energizer ultimate lithium.
At 15hrs and 10 min I noticed the light looked dim, when I turned it off, it would not turn back on.
Looking at the factory curve, the output decreases on high with time, from 80-60 lumens or so, using alkaline, probably why they used to call it 70 (and now call it 80).
With the lithium battery, it will maintain 80 due to higher discharge ability I bet, but that could shorten its time relative to what might expect from the alkaline performance, or it might not. Hard to say. Im going to do a high test tonight.
Higher current draw really strongly reduces the capacity of alkaline batteries(I suppose the batteries internal resistance dissipates it as heat), and the Li wont suffer this.