The city attorney office in LA has repeatedly said that the governor's anti-eviction order restricts local eviction measures. But the governor himself has said his order expressly permits cities to issue stronger eviction moratoriums:

Now that I'm thinking about it, the city of LA's eviction moratorium already goes beyond what the governor's order says. The governor's order is restricted to coronavirus-related nonpayment of rent. The city's policy also blocks lease violations for crowding, pets.