LOUISE: Who’s the dish? … He’s not of the manor born, that’s for sure.
Of the manor born means that someone is from an upper class or wealthy family. It is a common mishearing or deliberate pun on To the manner born, which means that someone is familiar from birth with a particular set of customs or behaviours.
The phrase is a quote from William Shakespeare’s Hamlet, which says, “But to my mind, though I am native here / And to the manner born, it is a custom / More honour’d in the breach than the observance.”
Louise likes to make literary quotes to show her intelligence, but she only chooses the most hackneyed, and in this case doesn’t even use it correctly.
The Annotated Gilmore Girls 