LORELAI: It’s like a Dean Martin Roast.
RORY: Those are never funny to me.
LORELAI: Yeah, they’re mean.
The Dean Martin Celebrity Roast is a series of television specials hosted by entertainer Dean Martin, airing from 1974 to 1984. For a series of 54 specials and shows, Martin and his friends would “roast” a celebrity. Roasting means to joke about and insult a celebrity, while also honouring them. The roasts were patterned after the roasts held at the New York Friars’ Club.
The specials were released on DVD, which is presumably how Rory was able to watch them. I find it unbelievable they would buy DVDs they didn’t find funny, or that they dislike “mean jokes” – Lorelai and Rory are both pretty cruel when it comes to humour. I can only think this is a little act they are putting on for Emily.