As mentioned, at least 12' at the lowest point.
Look at the specs for the lift. Example, my Bendpack HD9-XW:
HD-9XW Four-Post Lift - Tall Lift and Standard Width - BendPak
The runway height is 4.5", and the max lift rise is 82", so the max height is 86.5" (7.2 Feet) then add the height of your vehicle, plus and clearance above that.
A 12' celing would mean the car would need to be about 4'9" tall if lifting to the full lift height.
I have lifted my Ram 3500 (single rear wheel) with the lift, and the truck with the hood open is around 7'.
I think the 40' wide shop has a 24' ? (guessing) peak, that slopes down to 12' at the walls, and has 10' tall doors. The lift is away from the door, so the open door height is not an issue, and the door opens at the pitch of the roof, not horizontal. The workbench is along the wall, so the front of the lift is several feet from the wall.
If the shop is not very deep, you might want a roll up type garage door.