"They shouldn't mourn. She had one of the best lives ever," Lucie Arnaz said. "She is one of the few people we can look at and say she left us something that can help."
"I Love Lucy," which starred the redheaded actress as a zany homemaker and then-husband Desi Arnaz as her bandleader-spouse, first aired from 1951-55 and still is seen around the world on TV and on DVD.
Lucie Arnaz, 60, said she knows that Ball's legacy of laughter has proved uplifting.
"Every place I go, every country I'm in, I hear, `If it wasn't for your mother, I wouldn't have gotten through cancer. Or, `I was in a low point of my life and watched (the show) and laughed so hard, and if I can do that I can make it,"' Arnaz said.
She said the modest Ball always counted herself lucky to work with her husband, co-stars Vivian Vance and William Frawley and the show's writers, who mapped out the action for Ball's many wordless slapstick scenes that showcased the star.
But she was "the consummate clown of the universe," Lucie Arnaz added. Ball also had the right man at her side when she and Desi Arnaz pioneered the three-camera sitcom with "I Love Lucy" and founded the successful Desilu production house.
"She married this wonderful guy who made her better and who protected her and showed her off to her best advantage," Lucie Arnaz said.
The couple, who also had a son, Desi Arnaz Jr., 58, divorced in 1960 but remained friendly.
Desi Arnaz died in 1986 at age 69. Lucille Ball, born 100 years ago Saturday in Jamestown, N.Y., died in Los Angeles in 1989. She was 77.
Lucie Arnaz was asked by an interviewer from China this week to explain why her mother and the show are so popular there. It's a "phenomenon," Arnaz said.
"I think of her as Mom most of the time. Then I switch ... and try to see her as the rest of the world does. It's almost too big," Arnaz said.