You know what is really hard to find? A collection of Chinese Rail Timetables which are up to date, accurate, understandable and in English.
What’s more, the site carries a full list of fares as they will cost if you book them from the train station NOT after some unfeasibly high prices have been levied by the agency who hosts the train timetable, as is the case with most timetables I have found on the web.
Sooooo…As a result I have all the details I need for my train out of Lhasa. It appears that the latest date I can safely leave Lhasa is the 21st May at 0832 local time. That would bring me in to Guangzhou for around 1937 local time. From there I can get any of several frequent trains to Hong Kong from Guangzhou. As for prices I am looking at either 809 or 1251 RMB (104 to 161 USD) which is just fine and dandy with me.
Onwards with the planning!
Thanks to Flickr User Yewco for the stunning photo!