Zoe Kravitz and Harry Styles ‘Aren’t Attaching a Label’ to Their Romance, But They’re ‘Having Fun’

Zöe Kravitz and Harry Styles are leveling up.

After several weeks of PDA-filled outings in Rome, London and NYC, the inseparable duo proved it was more than a fling at a Sept. 6 lunch with Zöe’s dad, rocker Lenny Kravitz. “It was a thrill for Harry to meet Lenny,” says a source of their meal at Sant Ambroeus restaurant in NYC’s West Village.

“He’s admired Lenny’s music for so long, and the fact that he’s dating the daughter of one of his idols is pretty cool, if you ask him.” It helped that the “Let Love Rule” singer wasn’t playing the tough father during the meetup, says the insider. “Lenny doesn’t interfere in Zöe’s relationships, but he was keen to meet Harry.”

The One Direction alum, 31, and the Big Little Lies star, 36, were also together for dinner that evening — along with friends — and were spotted on multiple Brooklyn hangs the previous week. Still, the source says the new couple, who’ve seemingly gone from zero to 60, “aren’t attaching a label to their relationship yet, other than they’re hanging out and enjoying each other’s company.”

They’re both free spirits. “Harry checks all the boxes for Zöe and has a flair for fashion, which she admires,” says the source. “And she has a cool vibe that suits him.”

Despite their obvious chemistry, the source insists Zöe, who ended her engagement to Channing Tatum last year, “isn’t ready to get too serious. It’s casual, they’re having fun, and that’s all Zöe wants right now. They’re seeing where it goes.”