I think that in my modmod I'll let you build them in ancient forests, and require at least Iron Working to clear Ancient Forests at all. Elves would still be unable to build lumber mills.
Also, I'll eventually add events that cause lumber mills to clear to many trees, destroying the forests and the improvement (since there is nothing left to cut down and mill). There may be options in this event, some of which would really anger FoL civs/citizens in FoL cities.
I also added Forest Preserves from BtS, and gave them excellent synergy with FoL and Guardian of Nature. They can cause happiness, free specialists, and with Commune with nature will boost food and commerce. Plus, they help spread the feature they are on, including Ancient Forests.
I'm not sure I like that only FoL lands get ancient forests. I may change this, at least so that unowned land can have tis forests turn ancient, maybe all forests (perhaps only unworked forested tiles?). This would have to make the overall rate of changing be lower, but with forests preserves to spread them it isn't that big of a deal.
I'm also trying to decide whether I should include a lumber resource. If so, I'd probably make lumber mills create it and make it a prereq for later ships and siege units.