Truthfully, the Dalai Lama is much less concern to the Vatican than are the enormous and growing numbers of Chinese Roman Catholics.
The Chinese government insists on appointing Catholic bishops and archbishops, though these are illegitimate; as well as persecuting real Catholic clergy. They also periodically crack down on Christians of all kinds, with local and regional government razing churches, etc.
As far as numbers go, though officially atheist, 18.2% of their 1.4 billion population is Buddhist, and 5.1% are Christians. This means over 69 million Christians.