Cyndi Lauper on Time's Up and Singing with Kesha at the Grammys: 'We All Have Our Stories'

Cyndi Lauper is opening up about the Time’s Up and #MeToo movements.

In January, the pop icon stood alongside Kesha for her emotionally charged performance of “Praying” at the Grammys.

“I needed to — we needed to — stand up,” Lauper, 64, tells PEOPLE of singing with Kesha, Camila Cabello, Andra Day, Julia Michaels and Bebe Rexha. “It was really powerful … and good for her. I’m glad she’s doing well.”

Last year, Kesha returned with her smash album Rainbow, her first in nearly five years.

Since 2014, the “Woman” singer has been embroiled in a legal battle against producer and record label exec Dr. Luke, whom she alleges raped her. Dr. Luke countersued Kesha for defamation and breach of contract and vehemently deniesthe allegations. Despite widespread support from fellow artists and fans, a judge dismissed the assault claims, and Kesha is still contractually tied to Luke.

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Lauper — who will hit the road for a joint tour with Rod Stewart this summer — says she felt compelled to stand with Kesha at the Grammys for the powerful performance.

“Because I’m a female, and I’m a woman, and I came up in this industry, too,” Lauper says. “We all have our stories. It’s about time it’s done.”

Indeed, Lauper revealed her own experience with assault in her 2012 book Cyndi Lauper: A Memoir. In the book, Lauper wrote that in the ’80s, before her big break, her former bandmates assaulted her with a sex toy.

“He grabbed it, and then two other people grabbed me. I ran away from them, but they caught me and pulled my pants off. And the guy took the dildo, and he used it on me,” Lauper wrote of the traumatic episode.

RELATED: Cyndi Lauper Talks Performing ‘Praying’ with Kesha – ‘Sisterhood Is a Powerful Thing’

“I couldn’t believe it was happening. I tried so hard to break loose and I couldn’t, because I was being held down by his girlfriend and her sister — and she was a big girl,” Lauper wrote.

“I finally broke away,” she reflected in the memoir. “I was nauseated and in disbelief that it wasn’t just men — it was a guy and two women. I just could not understand why.”

Before performing at the Grammys, Lauper spoke to PEOPLE about why she supports the Time’s Up movement, an initiative and legal defense fund launched to help fight sexual harassment and assault in Hollywood and beyond.

For more on Cyndi Lauper, pick up the new issue of PEOPLE, on newsstands everywhere Friday.

“Sisterhood is a powerful thing and it’s important to stand with each other. And it’s important when someone is brave enough to come out and tell their story, you know, to support her,” Lauper said. “The Time’s Up movement is about equality in the workforce. Equality of power would change everything.”

Rod Stewart and Cyndi Lauper’s joint tour kicks off June 25 and runs through Sept. 21.