I just got new tires last Friday. I bought Michelin Primacy MXM4s from Costco. They have a special going until the middle of this month and they were less than $200 a tire.
I was talking to the manager as they were getting started, he said they do a couple of Teslas a month and complimented Tesla on a good design for putting on a lift. He said lifting one is easier than most cars and they've never had a problem. The Model S/X battery layout was designed for popping the car on a lift and changing the pack in a few minutes. As supercharging proved to be the better technology, they closed their one battery swap station and don't do them, but they probably put more thought into efficient and safe lifting of the car than most car makers.
The tech who backed the car out of the bay wasn't familiar with Tesla and had a lot of trouble getting it out. She'd get it moving about a foot and the car would go back into park. I don't know what she was doing. I thought something might be amiss with the car, but it drove fine for me. When the sensors calibrated they came up saying 35 psi and I had to go back. They thought they needed more calibration, but they only put 35 psi in the tires instead of 45. Fortunately I have an air compressor and put some more air in when I got home and all is well.
They had zero problems with the lift and no damage done or anything like that. Despite not putting enough air in there and the tech not knowing how to back the car out of the bay, everything else went fine.