If my relative was notitified by e-mail that her apartment lease isn't being renewed, is she still required by law to give advance vacate notice?

First, email is not the proper way to notify anyone that their lease is not going to be renewed; there should be some other kind of written notice that ensures that she would receive the notice, like posting it on her door.  She does not have to give advance notice of vacating if they are the one telling her to leave.  But first, I would check with the apartment manager and make sure that the email notice isn't a hoax.