You certainly could fly from Beijing to Lhasa, an one-way full fare Economy Class ticket (Y Class) should be around RMB2,400 (Less than US$300) if you purchase via a local travel agency or the airline ticker office in Beijing.

To the best of my understanding, Air China offers a daily flight between Beijing to Lhasa via Chengdu, the flight out of Beijing is CA4112, normally leaves Beijing at 07:10 and arrive in Lhasa at 12:10, operating aircraft would normally be either a B757 or A340.

For inbound flight from Lhasa to Beijing via Chengdu, CA4111 normally leaves Lhasa at 13:00 and arrive in Beijing 17:45. Again, operating aircraft would normally be either a B757 or A340.

Cheers.