LORELAI: But she [Rachel] seems sincere.
LUKE: How do you know?
LORELAI: Her nose didn’t grow.
Lorelai is referring to the 1940 animated film Pinocchio, produced by Walt Disney and based on the 1883 children’s book The Adventures of Pinocchio, by Italian author Carlo Collodi.
In the story, Pinocchio is a wooden puppet who is magically brought to life, and promised that he can become a real boy if he is brave, truthful, and unselfish. At one point, Pinocchio’s nose grows longer and longer every time he lies, until he promises to do better and has his nose restored. Ever since, it is common for people to talk about your nose getting longer if you lie.
Pinocchio received good reviews, and won the Academy Awards for Best Original Song (When You Wish Upon a Star) and Best Score – the first Disney film, and the first animated film, to win a non-honorary Oscar. It was a box office failure at first, but made a profit on its 1945 re-issue; it is now considered one of the greatest animated films of all time.