“Last Comic Standing” finalist Rebecca Corry is not joking about animal rights in Los Angeles … her nonprofit just sued the city, the cops, and Mayor Karen Bass, among others … over the unethical treatment of animals in city shelters and on downtown’s Skid Row.

All jokes aside … Corry isn’t just a comedian, she’s also an animal activist and founder of the Stand Up For Pits Foundation, which dedicates itself to saving the lives of pit bull-type dogs.

In the new lawsuit, obtained by TMZ, the foundation is suing Bass, the LAPD, Los Angeles Animal Services, L.A. Animal Services Manager Annette Ramirez, and the City of Los Angeles — claiming they’re all to blame for not following the law in caring for stray animals, and causing widespread animal suffering.

The nonprofit claims the city and its various agents consistently failed to follow and enforce various animal cruelty statutes, leading to widespread suffering … which the foundation claims led to the org picking up the slack and spending more than $50,000 to save and provide medical care for 11 dogs they say the city was supposed to look out for.

The foundation is seeking for the court to make the respondents commit to fulfilling their legal duties to the animals on their streets … and repay them for the money they’ve spent doing the city’s job in caring for the animals.