Yikes.
The most common type of lift around here is the kind where you drive up a ramp onto the lift, then off the lift again with the front wheels down a second ramp. When they start lifting, the car sits on rubber pads on the lift along its sides. Looks a bit like this one: http://www.youtube.com/watch?v=2tpFqyYE8yo, except the lift is shorter (the wheels are in the air), the posts are closer to the middle, and there are ramps on both ends. It can't possibly fall off, but would such a lift damage it?
In addition to "storage", the lift you show is often used for 4-wheel alignment ... but that's not the objective here.
pgwoosley makes some good suggestions. But I don't think the rubber pads on the suggested lift will do it. The aluminum frame is rather unique and unlike a regular unibody or truck frame. It's also not rectangular. I would NOT risk it. Unless you are 100% certain that the shop has the proper adapters for the rear, and knows to remove the floor pan first, then I suggest using floor jacks on the lift points as shown in the manual. And with that method I would keep two wheels on the ground at all times. The floor jacks will cost extra time and some inconvenience, but the extra effort is the price of risk and accident avoidance.
Final note: talk to a Tesla tech direct to confirm before actually doing it :smile: