I bought some cheap lithium primary AAA cells off of Ebay (http://www.ebay.com/itm/96-POWER-PLUS-AAA-LITHIUM-IRON-BATTERIES-6X-LIFE-OF-ALKALINES-NEW-/350560230384?pt=US_Single_Use_Batteries&hash=item519f049bf0)
60 bucks for 96 of them shipped. They seem to work well.
Here is a Thrunite Ti running on an alkaline: Thrunite buddle deal on ebay with offers
Here is the same light running on one of the lithium cells: 
The alkaline dropped to 30 lumens after 30 minutes. The lithium cell took about 80 minutes. It is interesting that the light output was increasing for the first 20 minutes. The jaggie lumen plot is because my sphere is currently set up for testing some monster lights (15,000+ lumens) and is in a very low sensitivity mode.