Adding Hinges to the Ice Box lid is a very popular upgrade. It allows access to the ice box without having to find a place to put the lid down. Removable hinges makes loading large items or cleaning the ice box easier.
Hinges are available at most Marine stores. They can be of the slide off or spring loaded pin type. Either style works. Depending on the model and other galley mods, the lid is held in the open position by a hook in the lifting ring or a folding leg arrangement.