In S1E4, Lorelai is yelling at Max and Headmaster Charleston about their refusal to let Rory take her test, and she tells Max, “You say she’s smart and she’ll do fine, and this rotting, stodgy rathole could use somebody like her, and then you completely shut her out of a test she’s been cramming for, that she’s ready for, that she completely deserves to take!”
Max, keeping his cool, tells Headmaster Charleston, “I didn’t call this place a rathole.”
Lorelai says, “Oh no, that’s true. I added that. Wouldn’t want you to get in trouble with “Il Duce’ here.”
“Il Duce” refers to Benito Mussolini, dictator of Italy from 1925 to 1942 (and Prime Minister before that, from 1922 to 1925). He is the founder of fascism. “Il Duce” means “the leader” in Italian. Mussolini led Italy to become one of the Axis powers in WWII. After being ousted by the King of Italy, he was eventually executed by Italian communists.