Jim, the inlay;
Before turning the box, the inlay material is selected, turned, sanded, finished, and parted off.
Once the lid and box are turned and fitted (very snug fit), the two are turned together to finalize your shape you're ready to fit the inlay.
Measure your inlay piece with dividers and mark your lid. With parting tool, carefully begin to turn an inset for the inlay. You will want to sneak up on the size of the recess so that you end up with an easy fit for the inlay to drop into. You don't want to force it in, but you don't want it sloopy either.
Once the recess is perfect (subjective for sure), a few drops of thick CA around the edge of the recess and spray accelerator on the inlay piece. Insert the inlay into the recess and hold for a few seconds to allow the glue to set. You can now turn and sand the top of the lid as a unit to blend it all together.
Apply finish on the whole outside.
Done!
Thanks everyone. The class was a blast and I finally learned the secret to fitting boxes.