Project Censored have an 2010 article titled The Media Can Legally Lie:
In February 2003, a Florida Court of Appeals unanimously agreed with an assertion by FOX News that there is no rule against distorting or falsifying the news in the United States. [...] During their appeal, FOX asserted that there are no written rules against distorting news in the media. They argued that, under the First Amendment, broadcasters have the right to lie or deliberately distort news reports on public airwaves.
Clearly, the story that FOX News got a court ruling in favor of its right to “lie” in its news broadcasts has become something of a talking point among the cable news channel’s detractors. There’s only one problem – the story as popularly told is completely false, and is based almost exclusively on hysteria, hyperbole, and half-truths.
There was indeed a lawsuit filed by journalists Jane Akre and Steve Wilson over their dismissal from FOX affiliate WTVT in Tampa, Florida. After that fact, however, the story is far different than how it is popularly portrayed.
Snopes also rejects this claim but its main reasons were that:
The TV channel involved in the suit was not the main Fox News channel, but an affiliate . (IMO, this is a cop-out.)
The issue at hand was not day-to-day programming, but a special episode involving Monsanto and bovine growth hormone (which seemed to be irrelevant to the question at hand.)
Fox News did not invoke First Amendment for its right to lie (which was not asserted by the claims.)
However, it did not cover the issue on whether Fox News won the second lawsuit, or if it even involved "the right to lie". In an example of a poor answer from Snopes, their quotation was not relevant to their claim that Fox News did not win the second lawsuit on "the right to lie".
Snopes also links to the 2003 judgment, which reversed the 1998 award. However, I was unable to fully understand the legalese behind this judgment, nor was I able to find a source which clears this up properly.
Being uninitiated in American politics, which article(s) is/are more valid?