FWIW there's two Broadway songs about the Lorelai from George and Ira Gershwin, both from flop musicals. "The Lorelai" from PARDON MY ENGLISH (1932) was recorded by Ella Fitzgerald circa 1960, and "Ukulele Lorelai" from TELL ME MORE (1925) has recently been released on a double CD containing TELL ME MORE and TIP-TOES (also 1925).

Also, the Moross-LaTouche THE GOLDEN APPLE (1954) contains a spoof of Rodgers and Hammerstein's "Bali Hai" about mythical sirens called "Goona-Goona".