The lid is two pieces glued up with an accent strip in between and then has some stringing (not to be called splines) added which are simply glued into the cut grooves or dado.
The grooves are cut along the grain and filled with strips and glue first; when the glue has set, the strips are sanded flush with the lid and then the grooves are cut across the grain and filled, which makes it easy to get away from cutting small pieces and a tight joint at all the intersections.
Now onto the corners, which are cut on a 45 degree angle, and a triangular spline is inserted with glue and here it is important to make the cut at the right depth so it will intersect with the innermost string inlay at the edge of the lid (see lid picture ); then the lid edge is sanded slightly so as not to shorten the spline as it would change the length.
A slight rebate is cut along the bottom of the lid to let it sit slightly into the box to keep the lid in place and alternately hinges could be installed.