I've mentioned before but didn't have the proof that you can place lumbermills in bad locations.

As you can see from the picture I was able to select a 2x2 area for lumbermill placement which cut across two different placement squares (the 2x2 area which counts as a set). As a result in the second picture I have no further building options even though it shows 4 placeable tiles available. The tiles are bisected in the forest area and you can't build anything else in the forest.

I believe the Lumbermill should have a snap-to position like other large developments which doesn't allow this to happen.