Turning this special box in a Humidor?

[prophetic_joe]

Put the cigars in the box, close the box, and run duct tape along the length of the seam.

Just from eyeballing it, it looks like all you need to do is create a "lip" around the inside of the lid. See how the lid has that border on it, then it's indented? I'd try to find some pieces of spanish cedar to fit on the inside of that border, really snugly. You probably want to mitre the edges so they fit together nicey-nicey. You may need to do this with elbow grease and sandpaper, since it's so small.

I'm not sure what kind of glue you'd want to use to tack it to the lid. I would think most glues would have some unhappy residual smells...

Bear in mind, I know next to nothing about woodworking

I agree just add a lip to it and you should be alright. get a nice tight seal. gorilla glue works great and I have never noticed any smell when it has dried.