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"We would likely use AAdvantage miles to travel business on a saver award, but I am not sure what the best routing would be to get to Lhasa."
You can't. No AAdvantage partner flies to LXA. Google "LXA airport wiki" to find the Wikipedia article for LXA airport; that article will list all carriers that serve LXA, and from which airports.
I'm pretty sure that the closest you can get with AA miles is KTM, which has scheduled service to LXA. Otherwise, your AA miles can get you to any of a number of Chinese cities (on AA/CX/JL) which have scheduled service to LXA.
Note that AAdvantage awards to KTM cost more miles than AAdvantage awards to China.