However, this week the 23-year-old took to Instagram to share some personal news with her followers.
Lily shared a trailer for upcoming HBO show The Idol, where she plays rising pop star Jocelyn in the six-episode drama.
VIDEO: Inside Johnny Depp's family life away from the spotlight
Lily wrote alongside the footage: "The sleaziest love story in all of Hollywood. From the sick and twisted minds of @samlev00 & @theweeknd , #THEIDOL coming soon. @theidol @hbo @hbomax."
Fans rushed to congratulate her, with one writing: "Beyond proud of you Lily," while another wrote: "You're killing it!" A third added: "I'm beyond excited for this show!"
The Idol was co-created by The Weeknd and Euphoria's Sam Levinson and Reza Fahim.
Lily-Rose Depp shared the exciting news of her new role on social media
While Johnny hasn't publicly congratulated his daughter, he no doubt has done in private, as the pair are incredibly close.
Throughout his recent defamation trial, the Hollywood star spoke fondly of his children on many occasions and was even wearing a bracelet with their names on it during the court case.
Lily-Rose Depp with her mom Vanessa Paradis
Lily has carved out a career in the acting and fashion world and previously had the sweetest - and funniest - reaction when asked about her dad on the red carpet back in 2018.
The star was asked by E! at the Chanel Metiers d'Art show whether she got style advice from her dad. "What's been the best style lesson from your dad?" the reporter asked, to which she replied: "My dad?! Erm, I usually look more to my mom for fashion advice."
Johnny is a doting dad to children Lily-Rose and Jack
Johnny - who shares Lily-Rose and son Jack with ex-wife Vanessa Paradis - himself shared some exciting news of his own on social media this week, posting a picture of himself getting ready in the trailer on the set of the film Minamata.
He wrote alongside it: "In the make-up trailer on Minamata, no on Digital & DVD in North America." He also recently released a single, 18, with Jeff Beck, following their tour around Europe.
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