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That will be tough to track down. L.L Co. made lenses for lots of makes and models as well as the aftermarket lines. Their lenses have been used on Desoto's, Plymouth's, and American Bantam, probably to name just a few. The 1008 is the model number. Here is a 1006 and a 2259. The 2259 is a Plymouth Lens from 1940. I don't know what the 1006 is from, probably a lamp like yours.
I have never been able to find an L.L. Co. catalog online. I had a Dirigible Spotlight from them years ago, used it as a spotlight on a 45 Harley that I built.