DL accepts "young lady", but I'm thinking that's incorrect, since "young" is too specific for basically "female gentleperson". (I put "young lady" without really thinking because of the Italian "signorina".)
So now I'm having a hard time too. Strangely, while I feel comfortable saying "That lady", I don't think I'd ever say "The lady".
One answer is that a ship can carry a boat, but a boat cannot carry a ship. Another is that a ship's captain gets annoyed if you refer to his vessel as a boat, but a boat's captain does not get annoyed if you refer to his vessel as a ship. :-)