Like the fictional Lizzie Eustace from Trollope's "The Pallisers" Lillie keeps her jewels with her while travelling.
Langtry, Texas, is not actually named for Lillie. Judge Roy Bean's saloon "The Jersey Lily" is named for her. Lillie did, eventually, go there. But not until after Bean had passed away.
Lillie purchased upwards of 4500 acres in California, which she owned from 1888 until 1906. Included on this property was a 350 acre vinyard, which is still bottling wine today. Look for wines with the Guenoc label and you will find that her face is still marketable.
The town of Langtry in Texas was built by the Southern Pacific Railroad (this also means that Lillie's line that there isn't even a railroad going there is another error) and was named after George Langtry, an engineer and conductor who worked for them. It IS a remarkable coincidence that a man who admired Lillie so much lived there.
Oddly, even though Joseph Horovitz is portraying the pianist Rubenstein in this episode, and, even though, we see his hands as he plays Beethoven's "Moonlight Sonata", they are not actually playing this work. They are too far down the keyboard and are striking the wrong keys for the music heard.
Lillie was actually fourteen when Longley wanted to propose to her.