The cover may have cleats on its underside, Fig.

285, C, which fit just inside the box and keep the top in place.

The cleats also prevent the top from warping.

This is a common Japanese construction, even in fine boxes.
The Japanese tie the top on with a tape or ribbon.
The lid may be boxed, Fig.

285, D, that is, portions of the sides may be affixed to the top.