It really depends on what the City will allow. Contact the zoning or planning department and ask them.
I doubt it -- but you would be very smart to contact the city's Department of Planning (email: Planning@lacity.org) to get a straight answer. While Los Angeles has a very permissive definition of "family," this clearly is a boarding house. You need to ask them if this use is allowed in this zoning district. And even if it is allowed (and I'd be surprised if it were), there still is the issue of how many people would be allowed per bedroom. Most cities use a property maintenance or building code that requires 70 square feet for the first occupant of a bedroom and an additional 50 or 70 sq. ft. for each additional occupant of a bedroom. So a bedroom in which 4 people sleep, would have to be at least 220 sq. ft. (280 sq. ft under the 70 sq ft standard). Those are some mighty large bedrooms and I'd be very surprised is a single family home in this zoning district would have bedrooms that large.
The bottom line is do not sit on your butt. Take action and call the Dept of City Planning. Give them the details and they should be able to let you know if this is legal. And if it is not legal, insist that the city contact your neighbor to let her know that she cannot do this.
The information provided in the question posed is not complete enough to provide accurate legal advice. More details are needed to really guide the questioner. My response is not intended to be taken as legal advice and does not establish an attorney-client relationship.