A simple way to create a lip is to use insert panels. Maybe just on two opposite sides, or all four. Just a short panel that matches the width of the sides, but shorter, glued in place. The top edge of the panel acts as a lip  for the tray to sit on, maybe 3/8” thickness so you don’t give up too much space inside. You could use cedar or something that smells nice as a bonus. I always think it’s kind of a nice surprise to decorate them too. 

Ryan/// ~sigh~ I blew up another bowl. Moke told me "I made the inside bigger than the outside".