Add a configuration and insert another instance of the hinge and lid, suppress the original lid and hinge, mate the new inserted lid and hinge, now you can set up mates accordingly so it closes at the closed position etc....
In the default configuration suppress the inserted lid and hinge...
Adding to John suggestions, I strongly reccomend you add a master sketch in your assembly which can be used to drive both box body and lid so you'd have better control later on when you add more parts to the assembly
after you have created the lid you can lock the external references. This will prevent the component from updating. The locked external reference can be unlocked again if an update is necessary.
SOLIDWORKS Product Definition Team
Thank you all for your input - I will definitely use those tips!