This is the original design, but decided not to go with it.
When I was cutting out the pieces I realized the darn lid would be pretty heavy and I didn't want anyone getting hurt if it came down unexpectedly. So I planned to add the gas shock lift to the design:

Here's a diagram of how I intended to build it (excuse the dimensions):

1. The upper attach point would be 7.5inches out from the hinge
2. The lower attach point would be 12 inches below the hinge and 4 inches to the left.
3. The cylinder I'd use is a 20 inch with 60 pounds of force.
But I sent my plans to my genius mechanical engineer brother and he redesigned the whole lid for me.