Bill Cosby is facing yet another lawsuit over alleged sexual assault -- only this time, it's from a woman who years ago had an infamously awkward interview with Don Lemon about her claims.

The comedian is named in a new suit that was filed by Joan Tarshis -- who's an actress and former comedy writer -- and she outright accuses Cosby of rape ... this after claiming he drugged her on two different occasions back in the early '70s.

In her docs, obtained by TMZ, Tarshis says she first met Cosby at the age of 19 through a mutual friend ... and got invited to the studio where they filmed the 'Cosby Show' for a one-on-one writing session.

She claims while alone with Cosby in his private bungalow there on the lot, Cosby gave her a drink, which she accepted and consumed ... only to start feeling dizzy shortly thereafter. Tarshis says she quickly passed out, and woke up to Cosby undressing her.

Tarshis says she was disoriented while she tried fighting Cosby off, and claims he overpowered her ... forcing his penis into her mouth without consent.

About a year after this, Tarshis claims Cosby reached out to her again in NYC ... offering to take her to a music fair he was performing at -- which she says she reluctantly agreed to.

Tarshis alleges she was given another drink while traveling with Cosby to the venue and she says she again started to feel weak ... and eventually lost consciousness. Tarshis claims she woke up naked in bed next to Cosby ... and that she felt she'd been penetrated vaginally and anally.

Tarshis is alleging assault, battery, infliction of emotional distress and false imprisonment ... and seeking major damages. Cosby's rep had no comment.

It goes without saying ... this is far from his first allegation. He's been sued numerous times over by countless women -- and even went to trial in Pennsylvania a few years ago ... where he was found guilty of assaulting Andrea Costand, only to have his conviction later reversed.