Hot glue dries up over time. You could use thick tacky glue and use spring clips to hold it in place while it dries. Or you could use E6000- which will set much faster or even fabric glue. Just pull your fabric taught while gluing. Also I would suggest using a very thin batting. A thick batting causes it to wrinkle in the corners of the slot. If you want it to look even nicer. You could cover the inside of the lid (after the top is glued in place) with felt or matching fabric.
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