It might be a Red-Lored Amazon, and it might not be a lost pet. The LA area has several parrot species that have escaped or been released by smugglers and have adapted well to the climate. I know a guy that had a flock of Macaws living in the palm trees near his apartment in San Diego as well.
There is even a flock of parrots that has been observed ranging free in San Francisco for several years now (subject of a book and indie movie, thought to have been released by smugglers at SFO).
This site has more info: http://natureali.org/parrot_project/ID.htm