Fox "News" is not a news channel. They actually define themselves as "entertainment" so you can't call them out for their lies in court.
This is the weirdest thing liberals believe. There is no such thing as "defining yourself as news or entertainment." There is no legal definition of "news organization".
The lawsuit you're going to reference said that Carlson was "opining" rather than stating "facts" which has a legal definition. Legal definitions don't often match with common usage.
And you can "call anyone out" for lying whether they're a news organization or not.