In recent weeks, CNN leaders were hopeful that Mr. Lemon would adjust to his new morning-show role and that higher ratings would follow.

On Wednesday, however, Mr. Lemon made headlines again after a highly contentious on-air exchange with Vivek Ramaswamy, a Republican presidential candidate. The segment deteriorated as the men fiercely debated questions of Black history and the Second Amendment; Mr. Lemon’s co-anchor Ms. Harlow could be seen sitting silently beside him, at times casting her gaze elsewhere and scrolling through her smartphone.

The incident left several CNN leaders exasperated, the people said.

Mr. Lemon joined CNN in 2006 from a local NBC station in Chicago. In 2011, he made waves when he acknowledged in a memoir what many of his colleagues already knew: He is gay. At the time, few national television newscasters were out in public. Mr. Lemon was upfront about what he described as the risks of coming out as a Black man, sharing his concerns “that people might shun me.”

“CNN This Morning” was a marquee initiative of Mr. Licht, a former morning-show producer, who succeeded Jeff Zucker as CNN’s leader in May 2022 and has overseen major changes at the network since Warner Bros. Discovery acquired its parent company in a media megamerger. Dozens of CNN employees were laid off, and some major producers and anchors left.

“CNN This Morning” has gotten off to a very slow start in the ratings, and struggled to keep pace with its predecessor, “New Day.” At an appearance last week at the Paley Center for Media, Mr. Licht said mornings were “the most competitive” hours in television.

“To launch a new show takes time,” he said. “And so it absolutely has had growing pains, and it will absolutely continue to evolve.” The program will now evolve without Mr. Lemon at the helm.

In a cheerful announcement in September, Mr. Lemon described the chance to host a new morning show as “a thrill” and praised Mr. Licht for selecting him. “I was honestly floored when Chris Licht asked me to do this, and I’m honored by his belief in me,” the anchor wrote at the time.

“Set your alarms folks,” Mr. Lemon added, “because we’re going to have a lot of fun.”