Lumber mills are probably disallowed from ancient forests for the same reason that ljosalfar can't build lumber mills at all- they don't fit for RP reasons. The treants that live in the ancient forests would probably get mad at you if you started cutting them up for building material (I know I would, if I were a treant).
So, how about putting in a special ancient-forest only improvement that mirrors the effect of the lumber mill? Call it, like, an "enchanted grove" or something and pretend that the added production comes from the forest spirits magically aiding your laborers. If the consensus is that the +1 food ancient forest bonus is too strong in conjunction with the production boost, perhaps the enchanted grove could even be given -1 food so that an ancient forest with an enchanted grove has the same yield as a forest with a lumber mill.