The 16-year-old is starring in Yoga Hosers, a horror-comedy about two yoga-avid girls planning to go a senior party, but who have to face monstrous forces when everything goes wrong.
The film's director, Kevin Smith, tells PEOPLE that Johnny, 52, met his match in working with his daughter. "It was adorable," he says.
"There's a scene in an interrogation room between the two of them and they're actually trying to out act each other and it's really cute," Smith says. "Then Lily busts out some French – because she speaks French really fluently – and just shows him up."
The film, which is a spin-off of Smith's Tusk, is a family affair for the director as well, with Smith's daughter Harley costarring with the Depps. Harley and Lily-Rose, who have known each other since kindergarten, had small roles in Tusk.
"At the end of the day of filming Tusk, Johnny was like 'If we were smart we'd retire and live off these girls,' " Smith says. "I took that rather seriously."
The film's producer, Kim Leadford from StarStream Entertainment, tells PEOPLE both of the girls "crushed it."
"They really rose to the occasion, and I think this will be something that will definitely launch their careers," she says.
Leadford says watching the Depps interact was "mind-blowing."
"They have such a sweet and funny relationship," she says. "They're buddies and they're really sweet with each other."
Depp's wife, Amber Heard, even came to set to surprise Lily with a dog during the holidays while filming.
Among other familiar faces in the film are Lily's mom, Vanessa Paradis, and Justin Long.
Smith says after 21 years of filmmaking, this is the most fun he's ever had.
"The whole movie is a real charm factory," Smith says. "It's just charm city, particularly watching a father and daughter act with each other."