Gypsy Rose Lee was the American burlesque performer of the 1930's and 40's who was the basis for the musical Gypsy. The term Rosie Lee is rhyming slang for the Cockney's favourite non alcoholic beverage, tea.
The use of rosie lee for tea seems to actually predate Gypsy Rose Lee by at least ten years and though its basis could possibly be from the military I can't find anything that would give it any kind of explanation other than it rhymes.
I do get to give you the fact that Gypsy Rose Lee appeared in an episode of the 60s TV series Batman as a journalist who interviewed Catwoman. So here is a picture totally unrelated to that fact, it is Rosie Lee though (I may be the first person to even call her Rosie!).