Notice my wording.

>If they refuse to stop

Implying you give them grace for a time and appeal to them kindly be it in private or public and try to get them to stop.

At some point the lies need to be delt with. A slanderous and lying tongue is an abomination to God.

I am not saying jump all in immediately.

But don't expect me to not ever deal with a unrepentant liar. I will expose them if they wish to not cease from the lying.

To think you are to sit there and take it is yellow belly cotton candy Christianity.

Paul exorcised a demon after days of it harping and telling lies.