When I lived there, there were vouchers to speuter that could be used at many, many vets if your dog came from a rescue. They may not have that county-wide program any more though.
I can't offer any personal recommendation of any of them, but there are LOTS of clinics that still free and low-cost services in Los Angeles -- here's a partial list:
Spay & Neuter | Los Angeles Animal Services
And another list of even more options:
Spay Neuter Los Angeles | NKLA
This one costs around $200, but they include go-home pain meds and an e-collar, which I think shows nice concern about after-care:
Prices ? SNP LA
(They also offer routine wellness care if you need it, at the same time...including $10 microchipping, which is also well worth the up-charge.)
If you go to a low-cost clinic, you DO want go-home pain meds for females. If they offer optional pre-surgery bloodwork for an upcharge, say "yes, please" (one high-volume spay/neuter clinic I know charges a mere $20 to add their surgery fee -- worth it!).
NOTE: In L.A., you shouldn't have to worry about vet students doing the surgeries because there isn't a vet school in the area as far as I know. HOWEVER, you might still ask and make sure the surgeons are all licensed DVMs, not vet students. I've seen vet students botch some speuter surgeries in horrific ways while doing rotations in animal shelters and low-cost clinics. Do NOT let a student do surgery, even under the supervision of a DVM. It's just not worth the risk. I have a $3,000 story about what a "free" spay cost our rescue when a student did it it in a shelter and nearly killed the dog.