Los Angeles, What Can I Do About A Landlord Who Refuses To Fix Anything And Threatens Eviction When Asked?

Location: Los Angeles

Hello, so I’m in a situation where I rent from what might be described as a slumlord, we’ve been in this apartment for many years and have had several issues that we brought to the landlord attention but was never fixed and instead was met with threats of eviction because “our rent is so cheap” or threats to raise the rent.
We also are the only occupants who pay extra for parking while being isolated to one parking space for a 3 bedroom while another tenant who is their friend has 2 parking stalls totaling 4 parking spots all to park 1 functioning car and 1 non operating car.

The things we requested be repaired is a leak from the roof where the upstairs tenant overfilled their bathtub, the water leaked through our roof causing damage to the ceiling, soaked into the carpet and wood is now uprooting from the spot that was soaked. After this we notice a horrible roach infestation. Also our front door lock gets jammed and needs to be played with until it opens which I feel like is a safety concern and we’ve had electric sockets that have been non functional for years.

When brought up again we get threats of eviction, rent increases and claims that we are somehow responsible for all of this and need to pay for things like carpet cleaning and electrical repairs. Recently they also made claims of us dirtying the backyard with no evidence whatsoever and claiming a visitor we have over occasionally lives there, again with no evidence and a threat to raise rent (directly after requesting to fix a leak under the sink)

My question is, how likely am I to get something done if I call the city and health inspectors out to inspect the apartment and on top of that, since I fear retaliation, how likely am I to win a harassment case? When I ask for a copy of our lease they don’t give us anything so I don’t even know our exact terms.

I have most of our conversations through text saved but i don’t have exact dates of repair requests and such. We even stopped asking about repairs because of the threats after mentioning them.

I’m mostly afraid of eviction or an order to vacate the unit for whatever reason that’ll throw us out of our rent protected unit.