She lived nearby is a complete sentence. If you want to use 'close' and 'near' you need to say what she is close/near to. She lived close to the station. 　She lived near the school. She lived near me/close to me.

Nearby is fine, and close is also okay, though I might use "close by" depending on the context. Near needs a point of reference. So you could say "she lives near me" or "she lives near the school." Near only describes proximity in relation to another place.