Unless I misunderstand, you plan to remove the lathe mnfrom the box, turn it upside down and store mkit in the box.
Sounds as if it could become a PITA. You would have to take everything out of the box, before turning it "right way up" to use the lathe. the shop could become like Rubik's Cube with everything having to be moved before and after using the lathe.
May I suggest leaving an opening at the "front of the stand, so that you can reinforce it to fit at least one shelf. What you store in the vbox will be accessible without having to disturb the lathe.
This is quite normal practice, for lathes from hobby ones to industrial ones. It makes for handy storage of spare chucks, chuck jaws, drill chucks, lathe tools, spanners etc. If you are careful, even DTIs and their stands.
Howard