The real story: Built in 1919 by actress Alla Nazimova, this was originally a home just for her, but when she needed money, she rented out the villas. The list of residents included Orson Welles, Ernest Hemingway, and Greta Garbo. Sadly, it was paved over in 1959. The Garden of Allah is also the name of a movie starring Marlene Dietrich, an actress from whom Jessica Lange drew inspiration from for Freak Show's Elsa Mars.
What could happen on AHS: A Reddit thread initially pointed out that Stanley mentions this hotel in Freak Show, and the blog Vixen Varsity revealed that a casting call for the season included a character named Carla, who fits Lady Gaga's description. Coincidence?