Hi fraidy! I don't know whether what she's said constitutes libel or slander... legally... but it sure sounds like online harrassment! At the moment, I don't know how many states have laws about this kind of thing... but since it's a fairly common thing, many sites are taking steps to police this on their own, voluntarily. Why don't you report her to FB?
You might get a form-letter reply, but it puts you on the record with them in case things go downhill from here. Report every instance where you feel you're being targeted. Then, step back and let the "management" handle it.
I do have a few questions for you, tho. Do you really think people are going to buy her brand of BS and believe her? People that know you well? Does it matter if people you don't know well, buy into crazy-talk? Isn't it likely, that she'll "out" herself for the malicious wacko that she is... all by herself? And all you have to do, is resist the temptation to get angry, fight back and defend yourself against sheer made-up crap... because if you enter the "ring" and start to duke it out with her - online or legally or whatever... you only become part of the sick side-show drama, right?
Might be time to give yourself a break from subjecting yourself to FB & her "preferred" method of harassing you. For a few weeks.