I couldn't come up with a better name for this box. But as the name suggests the lid hinge mechanism uses a 4-link design which I designed a few years ago....for a car's hood to be exact. I just needed to downscale the measurements by 10 and voila!
The hinge mount piece sit inside the top of the box on the "ledge". Place it right against the end with the two slots and with the rounded corner towards the middle of the box.
The hinge arms can be fitted with 3mm filament or something similar. The longer arms go in the lower mounting holes and the shorter ones in the top holes. You'll notice at the end of each arm is an extra rounded piece sticking out. At the box mounting end these must point down and at the lid they'll obviously point upwards.
The pics will hopefully give enough indication of how it all fits together.