LORELAI: You want him [Rune] to live here?
SOOKIE: No! Well, what about the old potting shed?
LORELAI: The old potting shed? That’s where Rory and I lived when she was a baby. It has memories and little rosebud wallpaper. I don’t want Boo Radley touching my rosebud wallpaper.
Arthur “Boo” Radley is a character in To Kill a Mockingbird, the 1960 novel by American author Harper Lee. He is a recluse who has been isolated from the townspeople since he was a teenager, and many rumours surround him. Boo Radley was apparently based on a real life neighbour of Harper Lee when she was a child. In the 1962 film version, he is portrayed by Robert Duvall [pictured].
Lorelai is saying that Rune is the town weirdo, like Boo Radley. The fact that she sees him this way shows that on some level, she is starting to accept him as a resident of Stars Hollow. (She can’t help it – she loves Stars Hollow, and on some level, everyone who lives there, even Rune).
It’s notable that after this Lorelai appears kind and friendly to Rune, a man she dislikes, who has been nothing but insulting to her, and is spreading rumours that imply she is his ex-girlfriend. Is she just being loyal to Sookie, or is there some fellow feeling with Rune, the black sheep of his family who has come to Stars Hollow with almost nothing? She gives Rune the same start she was given – an entry-level job at the inn, and some very basic free accommodation.
This is also the first we hear of Lorelai and Rory living in the potting shed at the Independence Inn, which will be important later in the episode.