First, in tandem with my question – posted earlier today – regarding cars offered during Golden Road from 1978-1983 and their prices (since they seemed lowball for a GR grand prize even adjusted for inflation), I'll suggest this particular Cadillac was offered early during the 1983-1984 season.
That said, I couldn't find any mention of an "L.A. Group" over on the oldcarbrochures.com website (where a whole bunch of classic car brochures are listed). My guess is this was a special trim-and-upholstery package, with special emblems, paint colors (unavailable anywhere else) and so forth, offered for just the Los Angeles market.
I say that as back in the day, Chrysler sometimes had regional specials for their more popular car models – cars painted a special color, special chrome trim/patterns, special seat upholstery and interior colors and other convenience features (unique, one-time items or those usually not available on that particular model). These were called such names as the "Western Special," "Ranch Special," "Texas Model," etc. (I realize some of those names may be made up, but you get the drift.)'
Brian