LORELAI: I thought he [Rune] was only here for a weekend.
SOOKIE: Yes, the lost weekend.
The Lost Weekend is a 1945 drama film directed by Billy Wilder, and based on the best-selling 1944 novel of the same name by Charles R. Jackson. It stars Ray Milland as an alcoholic writer, and Jane Wyman as his long-suffering girlfriend, and the “lost weekend” is a weekend vacation the writer planned to take, which turned into him losing himself in drink, and even being committed to Bellevue.
The Lost Weekend was the #11 film of 1945 and won four Academy Awards, including Best Picture, Best Director, and a Best Actor for Ray Milland. It also won the Grand Prix at the 1946 Cannes Film Festival, with Milland picking up another Best Actor Award; it is one of only two films to win the highest award at both the Academy Awards and the Cannes Film Festival.
Sookie doesn’t mean that Rune is an alcoholic; just that he was meant to stay with Jackson for a single weekend, but that weekend is long “lost” as he still hasn’t left some three months later.