Step 1 is find an LED with highest possible efficiency.
Underpowering LEDs typically leads to higher lm/W so a large LED like an XHP70-2 driven at low currents can get over 200lm/W while still outputting over 1000lm
Then you need an efficient driver, which I don’t have much information on, but you can find some efficiency tests if you look for them.
Finally you need a high energy to weight ratio battery, and the top ones are 18650 or 21700 Li-ION cells.
LG M50 or samsung 50E is what I would choose.
With this combo you could have over 3 hours of runtime at 1000 lumen output, or 6000 lumens for half an hour if you use mutiple LEDs.