The box was made by a friend of mine several years ago. It came with three shelves and was seriously water damaged, so I added a new front and back, sealed it up and made extra shelves. He must have had a router to make those nice cuts. My previous box supported the shelves with pieces of quarter-round.
I can't remember how I cut the hole in the lid because its been at least ten years ago, but the adapter came from the heating and air conditioning section of home depot.
Here's the underside of the weber lid