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.
claim they suffered damage to their face, head, neck, body and extremities.
Photos of Lucy, taken the day after the twirl, show lacerations to her arm that required stitches.
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.