"Dalai Lamas" is not a generic term. 'Dailai' (大理 or 大礼) refers to the Kingdom of which the lamas were servants. Fine for the rest of us, but for a Chinese Official to use this term 'Dalai' is to recognize, or is about to recede from this state.
Giving up or what?
Many countries have offered help to the defunct kingdom, when the Chinese used the term 'Dalai' in the past. The subsequent confusion has led to riots and acts of sabotage all over China.
Say what you mean man!
Note: The lamas don't rule, there was a King and a Court in the Kingdom. The Buddhist monks took over the palace when the King died.