If the rental property is illegal, does existing lease agreement become null and void?

Illegal is illegal. Illegal subject matters of contracts are generally unenforceable in Court. It is illegal for the landlord to lease the space to you and it is illegal for you to live in a space without a certificate of occupancy by the City of LA. I suppose the bigger question is what is your goal with this information? If you want out of the lease, then no problem. It is "Voidable" at your request. It is also legally "Void" as well. However, if you're goal is to stay there rent free, that creates a different set of problems because you legally cannot stay there at all since the occupancy of that structure is not as a dwelling unit. Also, an illegal garage conversion is not just "illegal" it could lead to criminal liability as well. If you contact the City of Los Angeles Code Enforcement Department (which by the way is a police department and some of the code enforcement officers in certain cities carry guns), they will be more than happy to visit the garage and issue a citation which will give the landlord a very limited time to either try and permit it or restore it back to the intended use as a garage. To answer your question, YES. It is illegal. But the bigger question is what is it you want to do with it? For that, you should see a lawyer.

Please see the case linked below discussing the Gruzen v. Henry case, which limits a landlord of a unit without a certificate of occupancy to the remedy of evicting non-payign tenants, and to not to unpaid rent. Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.