The call comes after Lord was sacked from CNN after he tweeted "Sieg Heil!" at the president of Media Matters for America.
Lord and Carusone have had many sharp disagreements.
Earlier this week, the two men got into a heated debate on Twitter over Media Matters' past financial support from investor and business magnate George Soros. Lord called Media Matters a "fascist" group after it launched a campaign for advertisers to stop supporting Sean Hannity, of Fox News, and claimed that it was trying to suppress free speech.
Carusone told Lord that one of his columns was "full of lies" and said "Soros gave us one donation one time.in 2010".
Wife of ousted Pakistani premier to contest for his parliamentary seat
Earlier, the former prime minister's caravan entered Rawalpindi surrounded by scores of supporters. The incident enraged the local resident who later raised slogans against Nawaz Sharif.
Mr Lord said Mr Carusone was playing a "fascist game" by targeting Mr Hannity's sponsors.
During the day, the Twitter sparring resumed, with Lord finally responding to Carusone with the tweet: "Sieg Heil!" "Why do you expect anyone to take you seriously when you don't take yourself seriously".
"I love CNN, but I feel they are caving to bullies here", he also told the network.
During his presence on CNN's airwaves Lord had frequently riled CNN hosts including Anderson Cooper and Don Lemon, fellow commentators, and viewers with many of his statements. "Jeffrey Lord is no longer with the network", CNN said in a statement. He was the first explicitly pro-Donald Trump commentator to join the network, back in August 2015, as a counterweight to CNN's other conservative commentators, who were all dismissive of Trump's candidacy. The network has since added pro-Trump contributors following the election.
"I mocked this guy".
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