We all know that she wants to own Pizza Hut Corporation, well probably.
But what she wants Lelouch to do for her, I don't know.
Morgan usually wants to defeat Arthur or Merlin because of some kind of natural cycle of kingdoms thing or some kind of Christian/Pagen conflict, when she is potrayed positivly. When she is potrayed negativly she just hates Arthur and or Merlin because she is Arthur's evil incestious sister.