...now it would be much cooler if I had found video of it, but it appears the film "Pa Says", with LB & Dorothy Gish is not listed in either the AFI or BFI OR Wikipedia. I found it listed in William Beaudine's assistant director filmography with Anita Loos as scenario-writer, in Marshall's pretty comprehensive 2005 book on Beaudine, who worked on quite a few 1913-14 Biograph shorts.
It has been listed on IMdB, but I know that's not considered always reliable. According to the PTB at IMdB, it was released July 21, 1913 and directed by Dell Henderson (TCM has Frank Powell as director, but Beaudine was working extensively with Henderson). Dorothy Gish (Dot) , LB (Teddy's Rival), Dave Morris (Pa) and Edward Dillon (Teddy) are in it. The short story Loos adapted was apparently "The Queen of the Carnival".
A summary in the Weatherford, TX "Daily Herald" of August 13, 1913, says "Pa says Theodore is a Lizzie Nizzy and won't let him Marry. Kate Teddy does a female impersonating act" (all capitalization theirs!).
I'm aware IMdB isn't always the most accurate, but I've been shamefully disappointed by AFI's list of Barrymore films (giving one of John's to Lionel, for example), so I'm prepared to go with this as one of his films, legitimately. Gish and Morris are both verified as being in the film by Motion Picture Story Magazine of August-December, 1913.