This 1957 video screengrab shows the same building on the right with the "BOWLING" blade sign. There's no mention of Carlin's, but the "SPORTS CENTER" signs match. This is east of Cherokee at 6624 Hollywood Boulevard, which was the Bert Goodrich Hollywood Gym and Cinema Sports Center in the 1956 CD (the cinema and a billiard parlor were on the second floor). It's been briefly mentioned on NLA a couple of times before - see
here and
here.
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Surprisingly, the cinema isn't listed at Cinema Treasures.