Lenny Kravitz Says He's 'So Proud' of Daughter Zoë's 'Iconic' Catwoman: 'Congratulations'

Lenny Kravitz is one proud dad!

The "American Woman" singer, 57, gave a sweet shout-out to his daughter, Zoë Kravitz, for her starring role in upcoming film, The Batman.

Lenny shared a photo to Instagram Wednesday of Zoë, 33, in costume as Catwoman. In the photo, she wears a black catsuit with her hair cropped short as she stares at the camera with intensity.

"Congratulations, my love, on this iconic moment. I am so proud of you. #TheBatman," Lenny captioned his post.

Lenny shares Zoë with his ex-wife Lisa Bonet, whom he was married to from 1987–1993. Following their divorce, Bonet, 54, married Jason Momoa, whom she split from earlier this year.

Momoa, 42, also showed support for Zoë in her latest role by attending The Batman premiere in New York City Tuesday. The Aquaman actor "made an extra effort to be there" for Zoë, a source told PEOPLE.

"He loves Zoë and always has. That hasn't changed," the source said. "He believes in family. He's always said that, and him going [to the premiere] is to show support for the family. That's what he does. And that's who he is. It's not more complicated than that."

Zoë stars alongside Robert Pattinson in the latest Batman movie, which comes from director Matt Reeves. She told told PEOPLE (The TV Show!)'s Jeremy Parsons that having the support of her loved ones has meant a lot to her as she embarks on her press tour for the film.

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"It's amazing to have people who love you show up at these major events in your life. It's really special," Kravitz said.

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Opening up about the process of playing Selina Kyle/Catwoman, Zoë recalled an early screen test with Pattinson, 35, who plays the titular character.

"The chemistry read was really intense," she told Entertainment Weekly. "Rob was wearing the Batsuit, and it was a proper camera test with the DP there and everything on a soundstage. It wasn't just reading lines in a room. So it was intimidating, to say the least."

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In a separate interview with Empire, Zoë explained the inspiration behind her character.

"We watched cats and lions and how they fight, and talked about what is actually possible when you're my size and Batman's so much stronger than me," she said. "What is my skill? It's being fast and tricky. So we did some really interesting floor work that incorporated different kinds of martial arts and capoeira and a kind of feline, dance-like movement."

She added, "This is an origin story for Selina. So it's the beginning of her figuring out who she is, beyond just someone trying to survive. I think there's a lot of space to grow and I think we are watching her become what I'm sure will be the femme fatale."

The Batman premieres in theaters March 4.