If the tenant is leaving voluntarily, you can rent out the unit just like any other vacant unit in Los Angeles. That is, still subject to the LA Rent Stabilization Ordinance. As @Steve Jones mentioned, you should keep up to date with the city requirements. As of now, you should be ok.
@Account Closed renting to anyone, whether through Airbnb or otherwise, could be very dangerous. The legislature recognized the potential for abuse of the Ellis Act and provided for steep penalties for landlords who do not comply with the requirements. The idea is that you are taking the units permanently off the rental market. A landlord's use of the Ellis Act is recorded with the county. An application must be made to the Los Angeles Housing and Community Investment Department before the unit can be offered for rent or lease, which would include Airbnb. If it's within five years of the unit going off the market, the unit would need to be offered at the same rates as before. Presumably, your Airbnb rates would need to be a pro-rata daily rate based on the prior rent, which would probably be too low to be worthwhile for a periodic rental. Additionally, you may have to give a right of first refusal to the evicted tenant(s) to move back in if the re-rental is done within two years.
You may be tempted to try to evade the law and rent out the unit(s) without going through the appropriate legal steps. This could be disastrous. If you are discovered, as a few landlords recently were, you could not only face a lawsuit from your tenants where they could recover the increased rent they paid, moving costs, etc., but you may be liable for punitive damages. Punitive damages are designed to punish a person for wrongful conduct and to deter others from engaging in the same conduct. While an insurance policy may cover your defense and potentially cover the actual damages of your tenants, it cannot and will not cover punitive damages. You could potentially be liable as an individual, without the protection of a corporation/LLC, and without the benefit of insurance coverage. I wouldn't evict based on the Ellis Act unless I intended to tear down the property or truly remove the units permanently from the rental market.