For some reason the bevel works fine everywhere (on the inside as well) except the rounded planks on the outside of the lid.
edit: I realized the problem was that there were some hidden faces in the wooden planks on the lid. In this case it should be possible to connect the object data of the planks to edit them all at the same time right?
We've had bevel issues crop up a couple times. Could you check this thread to see if the solution there solves your issue?