Answer: You very well may be able to sue your ex-wife. When someone lies and the lie hurts other people, even when it hurts only their reputations, the injured person can sue for slander and seek financial damages. In your situation, you may have an action for slander against your ex-wife if others heard the false statement and if it damaged your reputation or harmed your interests (for example, if it increased the amount of money you have to pay for child support). However, if you and your ex-wife have signed an agreement waiving your right to sue for anything that occurred at the mediation, you may have given up the right to sue her.
Another complication may be that you and your ex-wife signed an agreement to keep everything said during the mediation confidential. If so, the restrictions imposed by such an agreement may make your ability to sue her for defamation or other claims more difficult, because it may limit the evidence that you can introduce to show that she lied. If you are not sure about whether you signed anything that might affect your right to sue your ex-wife for lying about you, you need to talk to a lawyer experienced in defamation actions. Even if you did not sign anything, it is a good idea to see a lawyer before filing a defamation or other civil lawsuit.
The analysis would change if your ex-wife had told the lies under oath at family court, rather than during a mediation session. If that happened, you could not sue her for civil damages for the lies told during that sworn testimony. In general, witnesses testifying under oath are immune from liability for civil damages. Our legal system relies very heavily on witness testimony in order to function, and anything that might intimidate witnesses and prevent them from testifying is discouraged. So, this immunity is granted to witnesses testifying under oath in order to encourage people to testify freely and without fear of having to pay money damages because of the testimony.
But that immunity protects someone testifying only under oath. If your ex-wife told lies when she was not under oath,she is not immune from civil liability and you can sue her for those lies. And, if she has repeated those lies to your mutual acquaintances or family members, that may be slander, too.