The LM village is a very charming and walkable area to live in or around!
IIRC, the vast majority of the “granny flats” in that area are considered “grandfathered-in” by the city council and are legal rentals. Some even have separate addresses than the main house and some have a “Certificate of Non-Conforming Use” filed on the property.
Congratulations also on “inheriting” a good (longtime?) tenant!