See https://www.salon.com/2021/09/24/rudy-giuliani-lashes-out-at-fox-news-calls-his-ban-from-network-outrageous/
The alleged ban comes on the heels of a long-brewing legal feud between Fox News, Giuliani, and Dominion Voting Systems. Back in March, Dominion filed a sweeping $1.6 billion lawsuit against Fox News, Guliani, and host of Donald Trump affiliates for promulgating the former president's baseless allegations of widespread fraud in the 2020 election. The software giant argued that the channel "recklessly disregarded the truth" and "endorsed, repeated, and broadcast[ed] a series of verifiably false yet devastating lies about Dominion."
Also in the mix is Smartmatic's $2.6 billion lawsuit against Fox News, which alleges complaints of a similar nature, citing that the channel granted Giuliani a platform to spout unsubstantiated claims about election fraud. Fox has since filed a motion to dismiss Dominion's lawsuit and is also urging a court to shoot down Smartmatic's.
Giuliani, for his part, has backtracked somewhat on his claims of election fraud, saying back in August that his claims were "substantially true," while admitting that he didn't understand how Dominion's voting software works. Earlier that month, a 2018 deposition transcript was unveiled in which Giuliani effectively admits to the FBI that he had used Fox News to promote "fake news" about Hillary Clinton's campaign during the 2016 election.