I've seen a lot of YT videos on the subject of LCD/keypad modules. All of them are bare boards or breadboards. I also noticed at least one complaint about the futility of mounting the Arduino with shield in a permanent enclosure because of an inability to actuate the switches on the shield due to their short button.
After scouring the interwebs I think I have found a partial solution - if you don't mind a bit of LCD board modification.
I found some switches which can be had with different actuator lengths (up to 16mm). There are a couple of other options too. If you know the depth of your enclosure, a correctly sized actuator would protrude and be accessible through a hole in the cover.
I hope this helps.