I'm Lucy, and I'd be happy to answer your questions today. I'm sorry to hear about your situation.
You can absolutely sue your former customer for slander for making false statements about you and publicizing them. What you're entitled to is any lost business
as a result of her actions, plus punitive damages.
However, the First Amendment gives the media a little more protection than the average citizen. To sue a newspaper or media outlet for defamation of character, you have to be able to prove that they acted with actual malice. That means that they knew the customer was lying, or that they used reckless disregard in determining whether the story was true before airing it. That's a much higher burden than you'd have against an ordinary individual.
You do have the ability to ask the news outlet to air a retraction or your side of the story, which you did. If you show them any evidence you have that the woman is lying and they continue to air the original story without making any effort to determine whose telling the truth, then you might have a case against them. Because at that point, they're on notice that they should be investigating more carefully before they say anything else about the story.
One other thing: You didn't mention what the statements against you were. If they are OPINION statements, those are allowed. Under the Constitution, you're allowed to say your opinion all day long, even if it reflects negatively on someone else. Only untrue factual statements can be the basis for defamation.
It's important that you are 100% satisfied with my courtesy and professionalism. Thank you.