RICHARD: I’ll be right back.
LORELAI: Right back, Dad, like right back. In fact, change on the way upstairs. And make it a Navy shower – quick soap, quick rinse and no excessive posing!
A Navy shower is a method of showering that saves water and energy by turning off the water while lathering, and then turning the water back on to rinse off. The total running time of this kind of shower can last less than two minutes. Navy showers originated on naval ships, where supplies of fresh water were often scarce.
In US naval parlance, the opposite of a Navy shower is a Hollywood shower, which is a long shower that uses up a lot of water – I think this is what Lorelai is referring to when she says “no excessive posing” (like a movie star posing for photographs).
Most likely, Lorelai talks about a Navy shower because Gomer Pyle, previously mentioned in this episode, became the star of his own show, Gomer Pyle, U.S.M.C., which ran from 1964 to 1969. In this spin-off sit-com, the good-hearted Gomer Pyle joins the Marines, where he exasperates his drill sergeant with his frequent mistakes and misunderstandings.