Opened: The building now known as the Brentwood Theatre opened in 1942 on the Veteran's Administration campus as an entertainment facility for veterans. During the 40s the theatre was used for USO shows, movies and lectures. The photo is from Jeanne W. on the Yelp page about the theatre.
Also see the page about the larger theatre on the VA campus, the Wadsworth.
After 40 years of only sporadic use, the Brentwood got a renovation by Richmark Entertainment, headed by Richard Willis, in 2004. Following the reopening, Richmark managed the venue for over a decade booking legit theatre as well as occasional film screenings. They were also running the nearby Wadsworth Theatre.
Status: It seems to be in a dormant period. Richmark is no longer operating the building and seems to have vanished. The VA administration doesn't seem to want to talk about the venue.
A 2008 view taken from the back of the house by James Rosenthal for the Historic American Buildings Survey. It's in the Library of Congress collection. Thanks to Brad Lewis for finding the shot in the LOC collection.
See the Historic L.A. Theatres in Movies post for 40 images of the theatres used in the film including several more Brentwood shots plus views of the Wadsworth, the Crenshaw, the Leimert/Vision, the Orpheum and the Dorothy Chandler Pavilion.