This law/ordinance is unlikely to stand. California has a state preemption law, like Colorado. The NRA and SAF have used the preemption law twice to slap down a couple anti-gun ordinances in San Francisco. They are just wasting the taxpayers money by passing this law.
The OP's link says different...
"The Los Angeles ordinance is modeled on rules adopted in San Francisco and Sunnyvale that have so far survived legal challenges."
Lessons cost money. Good ones cost lots. -Tony Beets