Do any of Tallulah's biographies mention her friendship with puppeteer Burr Tillstrom? She was a big fan of his show Kukla, Fran and Ollie and Tillstrom even named one of his later puppets "Doloras," which I thought was in honor of her niece, but on this site I read "Doloras" was her poodle(???). Anyway, you can see Tallu, Tillstrom and Ollie's little cousin Doloras (along with a story of
Tallulah flashing Kukla and Ollie) at:

http://users.ultinet.net/~kfo/gommy.html