Three years into an acrimonious legal and public relations battle between the pop singer Kesha and her longtime producer Dr. Luke, who was once one of the industry’s most untouchable titans, the pair remain deeply, uncomfortably entwined not just in court, but in business.

On Friday, Kesha will release “Rainbow,” her first album since “Warrior” in 2012, chronicling, with an inspirational bent, her years of personal and professional turmoil on songs like “Bastards,” “Let ’Em Talk” and “Learn to Let Go.” But she will do so under the same extensive recording and music publishing contracts with Dr. Luke (born Lukasz Gottwald) that existed before she claimed in a 2014 lawsuit that he had for years “sexually, physically, verbally and emotionally abused” her. (Dr. Luke has strongly denied the accusations and no criminal charges have been filed.)

Though #FreeKesha became a cause célèbre — at its height, Taylor Swift said she would donate $250,000 to support the singer — and her comeback has been greeted by fans as a victory and a rebirth, it follows a string of legal defeats that prevented Kesha from releasing music outside of her deals with Dr. Luke. While her own contract claims were largely rejected by the court or withdrawn, she continues to face a lawsuit for defamation and breach of contract from Dr. Luke, who argues that her campaign against him has caused his work to dry up. (Though Dr. Luke has contributed to 40 Billboard Top 10 hits in his career, he has not been credited on one since 2015.)