FoL may not be particularly good as a permanent religion for non-Elves, but it works quite well as a transition religion.
1)
Idle forests become idle Ancient Forests for free. True, you can't lumbermill an Ancient Forest, but you do get +1
from the tile. If the tile was going to be sitting there doing nothing anyway then you're better off. In the early game I find that I develop resource tiles, and mine hills. Some riverside tiles will be farmed. Other flat tiles not high-priority for development until mid-game when my cities have grown large. Until then these tiles either aren't worked or are worked without an improvement on them. Only once all the high-priority tiles are developed will I go back and add lumbermills to the forested tiles, as an afterthought. Having those Forests upgrade to Ancient Forests is free food to help the city grow large faster. When it becomes time to develop the tile I'll just replace the AF with another improvement.
2)
Ancient Forests chop for more 
. When I do get around to replacing the AF I get more of a hammer boost from chopping it than if it were a normal Forest. This can add up to a considerable amount of
when deforesting around a city with many AF tiles.
3)
Priests of Leaves. While following FoL you can build several Priests of Leaves and keep them after you move on to another religion. They offer a number of benefits, including the ability to bloom tiles and summon tigers. Bloom will allow you to put a forest where you want it, either for another chance to lumbermill a forest tile before it upgrades to an AF or to preposition a forest on a tile that will then have a camp built in it (the other improvement that non-Elves can build in a forest tile). Tigers are okay as shock troops, but to my mind their biggest benefit is the ability to produce Tiger Cages in cities. +1
and +3
per city is a nice bonus for having followed FoL in the past.
4)
Woodsman II. The only way to enable this promotion is to follow FoL and research Ancient Paths. Often it is not necessary or even particularly useful, but if you plan to try to set up large areas of your territory with lumbermilled forests (some or all upgraded to AF) then you might need it to help with enemies that make it into your trees. It is nice to have access to the promotion even if your entire area is going to be deforested, however, if you have Elven enemies. Their territory is likely to be heavily forested, and so having some Woodsman II units can help you in a war against them.
5)
Refuge against Blight. There's an advantage to driving the AC up enough for Blight to trigger before your cities are large, especially if you expect the AC to end up reaching that level later anyway. If you can do this quickly enough then you can leave many of your forests intact, to provide further
to protect your cities. Once Blight has passed you can safely deforest your area without the danger of civ collapse from Blight penalties. If you are planning this strategy anyway then following FoL will help, because those forests you aren't chopping down will produce +1
if upgraded - which will increase the food available to the city and reduce the chance of starvation during Blight. Also, if you happen to research Ancient Paths then you can switch to Guardian of Nature once Blight triggers. This will burn off a few points of
while in anarchy, and also offer a
boost to overcome the Blight penalties. Once the danger is past you can switch to another religion and chop all those trees away (with extra
from AFs as compensation for production lost to anarchy).
Anyhow I didn't find it logical when Archery was made to provide lumber mills and +50%
