Malware is very common nowadays, and malware is very fast evolving. If the server is not using the latest software or upgrade, the chances is being "attacked" by malware is high. Most of the time, the attack is not even intentional. The malware just look for random servers to "hack".
The affected website is not even HH Dalai Lama's website. It is just a website related to Him. As such, it is highly possible that the website wasn't maintained well and as such "attacked" by malare. Therefore, just relax, nothing major is happening here.
Even if the attack is intentional, I am not surprised, because any person/organization with a lot of supports will also have a lot of people who hate them. Same goes to HH Dalai Lama.