The show has a lanai, too, although it was much larger, and covered by a veranda.
But here's a fact about Bea Arthur: NBC didn't want her to play Dorothy, even though the showrunners knew she was perfect. According to the suits, they thought Arthur was unpopular because she was very liberal in real life (and remained so until her death in 2009). She was the titular lead in the 1972 TV show "Maude," which included a controversial episode of Maude having an abortion, two months before the Supreme Court ruled on Roe v. Wade.
Susan Harris, the show's creator, and her husband, "Golden Girls" producer, Paul Witt, badgered the executives into letting Arthur star in the show, saying it was an ensemble piece, and that the show's success would not depend only on her.