So far as I know, there are trains from Hanoi to Nanning and Beijing but no trains are available directly to China from HCMC Vietnam. Thus, you could go to Hanoi first and then take a train to China. Or, you can take a flight from Ho Chi Minh City to Beijing first and then take a train to Lhasa. From Ho Chi Minh to Beijing, direct flights are operating on each Monday, Tuesday, Thursday and Sunday. And one train T27 is available daily on Beijing-Lhasa route. About the visa application, you could read China Visa(https://www.travelchinaguide.com/embassy/visa.htm) for more details, such as ‘Application in Your Own Country’ or ‘Application in a Third Country & Regions’.