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"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.

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