is it legal to drive without auto insurance in Los Angeles?

It is ILLEGAL to drive without auto insurance in Los Angeles and the whole state of California (and most of the other states in the US, too)
When you renew your automobile's annual registration, you have to submit a copy of proof of insurance of your car. If you don't enclose that in your renewal form, you will not get the new registration sticker and the document for your car. This is to ensure that the drivers and the car owners all have their cars insured.
You have to have at least "liability" insurance for your vehicle.

funny answer

that will depends on which part of LA