Semi-Mandatory on Chris’s design, fully mandatory on a simple top like Paul’s. If you are making it for live indoors, I would run a slight rebate in the lid so that when it close it is just recess a bit into the trunk. This will help create the seal both for dusty and “climate control”. One of the reasons a trunk helps reduce rusting is the will fitted lid seal. It slows temperature change down enough in the chest to help prevent “sweating” on metal tools. This means less chance of the tools rusting.
Lung T'an Hu Huesh Kung-fu Woodshop