Lydon, former singer of the Sex Pistols, is married to Forster's mother, German publishing heiress Nora Forster.
Arianna Forster, 48, was a member of the British all-girl punk band The Slits.
"John and Nora have asked us to let everyone know that Nora's daughter Arianna (aka Ari-Up) died today (Wednesday, Oct. 20) after a serious illness. She will be sadly missed. Everyone at JohnLydon.com and PiLofficial.Com would like to pass on their heartfelt condolences to John, Nora and family. Rest in Peace," the message on the Web site said.
"She influenced generations of women and created some of the most memorable music of our time, but Ari's true magic was how she affected people on the street, face to face, every day," the BBC quoted her manager Jeff Jacquin as saying on The Slits's MySpace page.
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