Yes, Loren is correct. Whether to take train or flight is depend on your ability to accomodate high elevation.
Some personal story. I visited Lhasa at age of 15 with my mom. The first two days I was tremendously uncomfortable plus I was told not to take showers during the first several days. My mom, who was about 50 years old, needed emergency medical care after two days of struggle. However, if you have no problem with that, then just take the flight, it's much faster and you can spend the extra time on sightseeing.

I have no idea how to apply the permission for foreigners, I'm Chinese

I think the most convenient flight back to NYC is CTU-SFO-EWR by United. United is the sole american carrier to fly to western China, and the price is usually resonable.