To be honest, I don't know anything about lithium air cells :thinking:
But as far as I know, more lumens in the same light can only be produced by a higher voltage cell. As most lights designed for Ni-mh cells can't even deal with the 3.7v nominal voltage of li-ion cells then you would probably need a different light for any higher voltage if the new chemistry offers that. Basically, the limitations on lumen output on most flashlights are due to what the led, driver and heat sinking can handle.
What advances in battery chemistry will offer in general will be an increase in
capacity stored in the cell. Meaning longer runtimes. Of course we can all hope that this will be mirrored by increases in led and electronic technology which will then be able to harness this capacity and turn it into more lumen output. Basically, the cell will be able to be driven harder and so flashlights could be brighter.
But if you want to stick it in a light you already have then it will either not increase it's output very much, or simply make it go