Since China visa policy got tight these days, you'd better apply in your home country or where you live for a long time. Chinese embassy in a third country may requires residence permit or visa valid for more than 6 months.
Chinese embasssy in kathmandu has released notice that for people who want to visit Tibet, they should apply to the Tibet Tourism Bureau (TTB) through travel agencies for travel permit, and then apply for Group Visa to enter Tibet with the Notification of Visa Application issued by TTB. Generally,it takes 5 working days for visa processing.