RSO-445 was a scheduled, Aero Asia flight from Muscat to Lahore. The flight was uneventful till it contacted Lahore approach at 0107UTC. The RVR was below the prescribed limit for ILS. The aircraft was cleared to land runway 36R. At flare out, the Captain lost contact with the runway lights due to fog. After touch down he drifted to the right of the runway on to the unprepared surface, where he rolled for abouJ 5400 feet before entering the runway. During this excursion, the aircraft knocked down a taxiway designator board at the airport and sustained damage to its right landing gear door and a few hydraulic lines. There was no injury to any person on board or on ground.