A Delta Airlines Boeing 737-800, registration N3748Y performing flight DL-1490 from Detroit,MI to Las Vegas,NV (USA) with 161 people on board, was enroute at FL340 about 60nm west of Omaha,NE (USA) when the crew reported a fire in a lavatory and decided to divert to Omaha. On approach to Omaha the crew advised that the fire was confirmed out. The aircraft landed safely on Eppley Airfield...