Somers lied incessantly for decades about the details -- which is why Ritter and deWitt stopped talking to her. I think they were right.
Lucille Ball had a "very tough" reputation. If she liked you (she liked Carol Burnett and Mary Tyler Moore) she could be incredibly gracious -- especially if she thought you were talented and that you were genuinely nice (like Carol Burnett and Mary Tyler Moore). But Ball suffered fools badly. And she was infamous with the service industry, she and her second husband, enabler Gary Morton. In restaurants and on airplanes -- they hated to see her coming. Nothing was ever right.
In the press, the story was planted that Morton approached her with the offer to do LIFE WITH LUCY and Lucy's face lighted up with enthusiasm. But others said Lucy's response was the precise opposite, with Miss Ball responding, "No way!"
But Morton had committed her, and Lucy reluctantly went along with it. That's the version I believe -- Lucy may have been a bitch on wheels (Elizabeth Taylor describes how Lucy kept screaming at her on the set when Taylor & Burton guest starred on HERE'S LUCY, Taylor adding snarkily about Ball, "But she's an icon...!") but Lucy was a smart woman, and knew LIFE WITH LUCY was not a good idea.
Interestingly, Lucille Ball hosted a THREE'S COMPANY retrospective -- she apparently respected the physical comedy of the show (presumably, John Ritter's).