Tropical birds have quite famously had a pretty big association with music. Take Iggy Pop’s delightful little Cockatoo who dances with him, trims his beard and just generally is the icon’s best pal.

Adding “World Famous” to the Parrot Lounge’s name might seem like braggadocio, until you check out the photos on the walls of the landmark Fort Lauderdale restaurant and bar tucked away in a little ...