Project Runway, the competition-reality show that launched a genre on Bravo, is flipping houses—unless NBC Universal (NYSE: GE) gets a court to back up its claim to the show. The Weinstein Company and Lifetime announced a deal today to move the show to the women’s net for five years, starting with its sixth season this November, complete with supermodel host Heidi Klum and fashion guru Tom Gunn. (Klum is the one who kisses off losing contestants with “auf wiedersehen.")

It’s a major blow to NBCU, where Project Runway is the heart of its Bravo reality competition slate including Top Chef, Shear Genius, and Top Design. NBCU claims it had first refusal and filed suit today in New York state court. Weinstein Company lawyer David Boies:  “We believe that this lawsuit is without merit. While good for the market for lawyers, it is always unfortunate when parties try to…