I don't have the exact URL to hand, but Google for "Prometheus Music" and "Hope Eyrie". Also, possibly not strictly legal, there's interesting stuff found under "anime music video". You might be surprised how little lip sync is really needed. Not all music is locked up by the big companies, and a music video is a lot less intimidating a project. It might also be possible to record a performance of out-of-copyright music -- talk to music teachers.