A lavatory is a bathroom or a restroom. You should go to a restaurant's lavatory to wash your hands before dinner.
Lavatory is a slightly formal way to say "bathroom." Most people would never refer to this room in their own homes as a lavatory, although they might use this word for public restrooms in schools, hospitals, or other buildings. In the U.K., a lavatory is just a toilet, and its earliest meaning was "washbasin," from the Latin root lavatorium, or "place for washing."