Were you aware of the Musart Theatre at 1320 S. Figueroa? Me neither, until very recently.
It was a little legit operation that was around for about 40 years. In fact it probably opened under the name Little Theatre. It was also known as the Egan Theatre, after a noted acting teacher of the time.
I can't locate any photos of it. You'd think some of the local archives would have a photo of that block of Figueroa but so far nothing has surfaced.
The poster here is for a show sometime between 1936 and 1941 as part of the WPA Federal Theatre Project. You'll find a larger view on the Library of Congress website.
I started a page on the Musart Theatre but it's rather sketchy so far. Let me know if you come across anything you can add to my account of this mystery building.
It also may be of interest to check out the page on the Beaux Arts Theatre on the Wilshire Boulevard Theatres site. It was another venue for Federal Theatre Project presentations.