"I am going to sue Twitter on multiple grounds", Stone told Business Insider on Sunday.
Twitter's abusive behavior guidelines stipulates that accounts in violation of its policies could be subject to a permanent ban.
Stone told NY magazine, which first reported the news, that he had been advised he has a "very strong legal case".
It is one of the highest-profile account suspensions since Twitter has said it will take stronger action against bullying and threats of violence on its service. He used an expletive to describe the political pundit Ana Navarro and wrote that Jake Tapper, who hosts "The Lead" on CNN, "must be held accountable for his lies and very severely punished".
Stone's tweets, which have been archived by Deadline, referred to Lemon an "ignorant lying covksucker" and saying Lemon "must be confronted, humiliated, mocked and punished".
Stone has known Trump for decades and acted as an adviser during the early days of the Trump campaign. Since Stone's account is suspended and he was reportedly banned permanently, the original tweets can't be referenced directly. And since the election, Stone has been a stalwart ally of Trump, attacking the president's critics on Twitter and elsewhere. "After twitter found that a tweet of mine, I was informed that I was suspended for three hours and 22 minutes, "he wrote on Facebook".
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He told the hosts of a USA radio interview: "To be honest at first I wasn't having it, I didn't understand it and I wasn't sure. "We're all edging for her to get back to work, it's just finding the right time and the right way to do things".
Sunday morning, Stone told Politico that his suspension was "part and parcel of the systematic effort by the tech left to censor and silence conservative voices", and that he had made a decision to pursue legal action against Twitter after consulting legal counsel. That suspension and did some time ago yet my Twitter feed is still not functional.
During his Twitter rant, Stone called CNN anchor Don Lemon "dumber than dog shit", "a tiresome witted arrogant partyboi", and an "ignorant lying covksucker". He says in the Netflix documentary Get Me Roger Stone that he got Mr Trump to run for president.
"Twitter wants to avoid being regulated like a utility", he told the publication.
Since then, Mr Trump has tried to put some distance between himself and Mr Stone, who regularly appears on network television to support his former employer. No one has been willing to file the antitrust case.
But don't expect Stone to hand over his right to tweet without a fight.
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