An Arik Air Boeing 737-700, flight W3-596 from Owerri to Lagos (Nigeria) with 69 passengers, was climbing out of Owerri when the right hand engine ingested a bird. In the absence of any abnormal indications at first the crew decided to continue the flight to Lagos (231nm west of Owerri). While enroute the engine developed serious vibrations prompting the crew to shut the engine down on approach to Lagos, where the aircraft landed safely.