The actress, who joined the Channel 4 soap earlier this year as Jenny, admitted that she didn't want to achieve success simply by using Lacey's EastEnders fame.
"It would be embarrassing to walk into an audition and say that," she told the Liverpool Daily Post. "Every time I went to an audition, I never mentioned Lacey, because that would make me sound stupid.
"I am used to Lacey being in a soap so people are bound to ask about her. But this is something I want to do on my own."
Younger sister Lily Harvey, 10, had a role in EastEnders, playing the daughter of Kat Moon's [Jessie Wallace] friend Martine [Tamara Wall].
"All three of us do it," Daisy added. "Lacey and I acted as kids. Our mum, Bev, let us do everything - singing, dancing and acting.
"I was at home with my mum and sisters when I got the call to say I'd got the part. Lacey said if I need her, she is there."
Daisy recently admitted that she felt under pressure to impress Hollyoaks fans while filming her debut.