It's true. Renting a house in Lhasa is highly speculated. Have you ever been to Lhasa? If so, I suggest you find a youth hostel or something for a few days, and then discuss it with a private family. I went there last year and found one. It is still near Jokhang Temple. Which one was very hospitable, and finally I stayed for a month and gave him 300 yuan. Now I have lost his address book, which is a pity.
But that was a year ago. I don't know if there are any more. I'm just telling you my experience, hoping it will help you.