The actress-turned-singer, 42, has been dating Rage Against the Machine drummer Brad Wilk.
"They are a thing," a music source told the New York Post's Page Six of their relationship.
A rep for Lewis did not immediately return PEOPLE's request for comment.
Lewis first hinted at the blossoming relationship on Instagram five weeks ago. She posted a shirtless photo of Wilk, 47, playing the drums and captioned the shot with three hearts.
Shortly after announcing that Wilk would join Lewis on her band Juliette and the Licks' European tour, she shared a cozy shot of the two, calling him her "honey."
Since then, Lewis hasn't been shy in flaunting their affection on social media. She's posted several sweet snaps of the two cuddling in bed, with the caption "LOVE IS REAL," as well as using the hashtag #DomesticBliss on another shot.
While kicking off their tour in Berlin, Lewis shared a short clip of them walking down the street – and sharing a quick kiss.
Wilk also showed his affection for his new love on Instagram, posting a selfie of himself wearing a souvenir shirt from the Juliette and the Licks tour with Lewis' face on the front.
"Beautifully Fierce, Force of Nature, this one," he captioned the photo.
The two were also seen walking arm-in-arm during an afternoon outing in New York City on Saturday.
Lewis was previously linked to fellow musician Travis McCoy in 2012, while Wilk separated from his wife Selene Vigil-Wilk in 2013 after eight years of marriage. The former couple have two young children together.
Lewis and Wilk performed together at the Tribeca Film Festival on April 15, and are currently on the Licks' European tour.