If youre putting the hinge inside so that it is not visble, you need to inlet both box and lid.
Use a vernier to measure the thickness of the hinge at the pin. divide by 2. Thats the depth you need to inlet.
measure the distance from the centre of the pin to the rear of the hinge. Thats the distance back that the inlet needs to be.
make sure your screws are small enough that the head fits flush inside the countersink on the hinge, or they will force the box open.
You can err a few thousandths of an inch deeper on the inlet, as you can always pack it back out with a piece of paper or card, but if youre not deep enough you have to start all over again.