From the Y-like shape of the female crotch.
dine at the Y (third-person singular simple present dines at the Y, present participle dining at the Y, simple past and past participle dined at the Y)
- (slang) To perform cunnilingus.
2015, Rachel Redhead, Curse-Breaker Origins - The Vampires: Debbie Fall, page 158:
“Then let us have sex, right here next to her body. Let me dine at the Y now. I'm hungry for some girl juice.”