I was finally able to track down some definitive photos of the LARY/LATL First and Chicago Streets loop. Yes Margaret, there really was a transit loop at this location.
First up, for reference, the original photo. If you look carefully at the rear of the car closest to the camera you can see the rails curving to the right, behind it.
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Photo 2., is a Google Street View image showing the buildings on first street that are visible across the triangle in the original photo, while photo 3., is a GSV referencing the current vest pocket park.
Photo 4., is from the Andy Goddard collection on the pacificelectric.org website and shows a March 1963 LAMTA excursion at the the loop where it curves up alongside the brick building still extant and facing the park. These are the rails seen behind the car in the first photo.
Photo 5., is also from the Andy Goddard collection an shows the same scene from the passenger boarding side of the cars.
Now to see if I can track down the location of the PE Butterfly 12 at Compton, from ER's post No. 27287. . .
Cheers,
Jack