If you want to know the origin and meaning of this idiom, you have to start with a distant story.
Now, everyone knows the origin and specific meaning of the idiom "the lips die and the teeth are cold". When we describe the close relationship between the two sides, interdependence, and no one can do without each other, we can say that our lips are dead and our teeth are cold, and we can also say that our lips and teeth are interdependent.