expired Singapore Return to Lhasa, Tibet $542 via Sichuan Airlines (March-May 2018)
Sichuan Airlines are offering cheap flights to Lhasa, Tibet for $542. Fares include bags, meals and seats. There is a stopover in Chengdu, China on the way. Dates are from March to May.
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I've also found some a cheap flight for $323 return via China West Air from Dec 28 to January 2 which would be a cool short trip for New Years. However, bags, meals and seats are extra and the website is very difficult to figure out. If you can speak Chinese and have the patience to navigate through a bad website then check it out.