I can actually agree with both sides of the argument for the lumbermills being at archery, and for them being at iron working.
On the archery side, there's the game-balance issue of spreading out all the improvements and buildings over more techs... After all, how many are down the metal line? I know there's notably more than the archery line. Also, there's the fact that archery is considered to be more of a wood-working tech, although bows are normally made, now, out of metal or composite materials. At one time they even used bone for bows, as I recall.
As for the Iron Working side, there's also game balance to be had. People seem to consider lumbermills rather powerful improvements, and in a way, they are. +1 hammers, maybe +1 commerce (I forget, but I think they have a boost on riverside) AND you get to keep the forest's health bonus for the town? That's not really something to shake a stick at. However, you also have to think about how a lumbermill works. From my understanding of them, they use a large circular METAL saw blade to cut the trees into appropriate size segments, after they've been chopped down of course. Not only does this need to be a rather strong metal to not chip or bend every time, thus why copper/bronze isn't exactly ideal, but it also needs to be repairable and replaceable, thus needing iron working instead of just smelting.
... Personally, I'd rather it be archery myself... I use them all the time and having to wait for them to build for so long is annoying, but I think having it at iron working makes more sense.