I searched Los Angeles, CA and found 101 shops in the general search.
When you did the advanced search with the make Lexus or Toyota it only shows one shop. That is probably because not many listeners checked the box for Toyota or Lexus when posting.

I would scan the list of 101 for any that state Japanese or Import specialists or something similar and cross check on Yelp/Google. However a lot of their reviews are very old and I consider it just a starting point before looking elsewhere. You may even want to look at our Club Lexus regional forum section to see if anyone recommends shops.
https://www.clublexus.com/forums/pacific-25/
You may want to try some Yelp and Google searches and maybe use the name of whatever local area around Los Angeles that is close to you.

 

I have picked up some knowledge about various engines(Japanese,German, American, Korean,etc.) over the years; which generally does apply to all more or less.

 

You'll need to find a good indy shop & get your vehicle hauled out of that stealership fast......