The hopeful, who will appear in tonight's episode of The Voice, said: "I didn't want my parents brought into it. I didn't bring my mum and dad with me. I wanted it to be about me.
"I didn't want to only be Linda Lusardi's daughter if I didn't get through," she told the Daily Star.
The 20-year-old model's audition will be shown later as the ITV singing competition enters the fifth week of blind auditions.
Model Lucy said she didn't want mum Linda stealing the limelight at her audition for The Voice 2017
Lucy will appear on tonight's episode of The Voice singing Will You Still Love Me Tomorrow
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She brought her boyfriend Joe and brother Jack along to her audition instead, where she sang The Shirelles' Will You Still Love Me Tomorrow.
Lucy is the daughter of Linda and 48-year-old former Brookside and Coronation Street actor Samuel Kane.
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A former glamour model and actress, Linda, 58, was voted the best Page Three girl of all time in 2005.
Lucy recently posed in her underwear for The Sun, but admitted that she couldn't follow in her mum's footsteps as a topless model.
Lucy is a model like her mum but says she could never pose topless
Lucy carries on her family's showbiz nature and is a singer, actress and model
"I don't have the assets for it like my mum, I'm not gonna lie," she told the newspaper. "I think it's great that women are confident enough to do it and it is what it is.
"I'd never go topless. I just don't think it's for me."
Lucy revealed that Linda spoke to her about her former work as a glamour model and admitted: "I did have a few boys say my mum's a 'MILF' but everyone gets that don't they?"
A source told The Sun that the panel were "blown away" by her performance, saying: "Lucy's got the whole package – showbiz is in the family but they didn't know."
The Voice UK continues tonight at 8pm on ITV.