What does a "lips and teeth" diplomatic relationshp mean?

"If the lips are gone, the teeth will be cold"

This is a Chinese proverb meaning that if one of two interdependent things falls, the other will be in danger.

This "lips and teeth relationship" is a relationship of interdependence. China and North Korea have long enjoyed this kind of political and economic relationship, with China being "the lips" (the protective partner) that prevent "the teeth" (North Korea) from being cold.

• The idiom derived from a story in the Spring and Autumn Period, when the State of Jin sent an envoy to the State of Yu with a lot of money and goods on a mission to persuade the State of Yu into agreeing to Jin State's request for attacking the State of Guo via the Yu State. The stupid Duke of Yu agreed. One of his ministers learnt it and said: "the State of Yu and the State of Guo are like lips and teeth. If the State of Guo is wiped out, so will the State of Yu". But the Duke of Yu turned a deaf ear to him. In the end, the State of Yu was indeed wiped out by the State of Jin shortly after it destroyed the State of Guo. -- from Cultural China