You can make the four sides of your lid frame & assemble together leaving an open center section. Then use a rabbit bit with a bearing & route a rabbit around inside parameter. Depth set to thickness of center section material. Use a chisel to square up your rounded corners from the machining process with the bit. Cut your center section sized to fit the rabbited section. Your center section should fit the recess & be flush with the frame.
Do you have a picture of your box?
Have a nice & safe day!
Last edited by jlord; 03-02-2010 at 10:31 PM.