In the lawsuit, obtained by TMZ ... Lucy Pavlovsky and Nadia Beddini claim they each suffered permanent injuries in the bottle-smashing fight inside W.i.P nightclub in NYC on June 14.
Both women claim they suffered damage to their face, head, neck, body and extremities.
TMZ obtained photos of Lucy, taken the day after the brawl -- which show lacerations to her arm that required stitches.
In the suit, both women point the finger at the people who ran the club ... claiming the bottle-throwers were "sold and consumed alcohol in excessive amounts" ... even after they appeared wasted.
In the suit, filed in state court in New York by attorney Javier Solano, the women also claim the club failed to properly train its bouncers to handle a violent situation.
The women are also suing the bottle-throwers -- but since their identities are still unknown, they've listed the culprits as John Does 1 through 5.
The women are suing for unspecified damages.
Neither Chris Brown nor Drake are personally named in the suit.
A rep for the club tells TMZ, "We work hard to provide a safe environment. If an accident or injury occurs we try to respond appropriately. We will review the claims in this lawsuit and address them in court."