Let's see if you can follow my ASCII diagram...
A--->|
|
|
OB
C O---->D<----(Lid)
Image a triangle (bellcrank) made of BCD, with C being a pivot. There is a verticle member going up from B that pivots... there is a horizontal member from D attached to the Lid with a pivot.
If you apply a force (A) down on the lever connected to B, the bellcrank will rotate about C, making point D rock CCW. This motion would open/close your Lid. There are a zillion combinations of this system that are used in even more applications in almost everything. Playing with the ratios between BCD will give you different mechanical advantages and movements. "Happy the Hare at morning for she is ignorant to the Hunter's waking thoughts."