“L tattooed on her forehead”

LORELAI: And these fanatics that run your school, they’re the ones that write the letters to the fancy colleges saying things like, ‘Hey she’s keen, look at her’ or ‘Have you seen the L tattooed on her forehead, ’cause it sure is a big one.’

Lorelai is referring to the habit, very common in the 1990s, of satirically making an L shape with the fingers on either your own or another’s forehead to denote you or they were a “loser”. Lorelai imagines the L to be tattooed on Rory’s forehead as a mark of permanent loserdom. Loner and loser seem to become conflated extremely quickly in this episode.