Lionsgate filed suit in Los Angeles Wednesday against The Weinstein Co., preemptively claiming the latter has no rights to the Sundance sensation “Push” — not to be confused with the movie of the same title starring Dakota Fanning — which Lionsgate announced it had picked up earlier this week, in association with Oprah Winfrey and Tyler Perry. TWC’s mouthpiece tells the Hollywood Reporter his clients had a deal with the film’s sales agents, who turned around and sold the Harlem-set drama starring the award-winning, Oscar-buzzy Mo’Nique to Lionsgate after it made a better offer. Most likely, TWC (which keeps denying it has cash flow problems) will be happy to settle for a logo and a piece of the action, an arrangement they have made with other studios in the past, including Fox Searchlight on “Garden State” and “Under the Same Moon.”