Your taxi driver was a bit over optimistic on the mileage - in both Lanzhou and Lhasa. Leastwise from my visit in Oct 2003.
In Lanzhou we took the local bus - much to the dismay of the taxi drivers. Quite reasonable price though it sat at the terminal for quite a while. Maybe 40km. We took the train to from there to Xining and onward to Golmud.
Lhasa might be 60km from the airport. If you are going from the city to the Nepal border you will pass it several times. No ideas on the taxi prices there as we took the overland route into town from Golmud. Still a better idea for acclimitization...... If you have the time.
YMMV - but wander happily whatever route you take (or get stuck with)
Fred