If you are using a carbide cutter to cut the threads you should have no problems with the Corian, some colors and composites turn better then others, all depends on what they mix the polymer with when they cast the material. You normally want to cut the threads in several successive passes cutting the threads deeper as you go. You also need to adjust the speed of the cutting tool and the speed of turning the work piece so you are not heating the Corian as you cut the threads. I glued cut rings into the box and lid and threaded them as you would a typical wood box and lid. The rings were usually 1/4 to 3/8 tall by 1/4 to 3/8 thick, you can cut these on a lathe or cut them with a hole saw on a drill press, you usually sand the surface to be glued with coarse grit sand paper to provide a surface that the adhesive can bond to.