Since the early 1920s, there has been speculation that Davies and Hearst had a child together some time between 1920 and 1923. The child was rumored to be Patricia Lake (nee Van Cleve), who was publicly identified as Davies' niece. On October 3, 1993, Lake died of complications from lung cancer in Indian Wells, California. Ten hours before her death, Lake requested that her son publicly announce that she was not Davies' niece but Davies' biological daughter, whom she had conceived with Hearst. Lake had never commented on her alleged paternity in public, even after Hearst's and Davies' deaths, but did tell her grown children and friends. Lake's claim was published in her death notice, which was published in newspapers.  Lake told her friends and family that Davies became pregnant by Hearst in the early 1920s. As the child was conceived during Hearst's extra-marital affair with Davies and out of wedlock, Hearst sent Davies to Europe to have the child in secret to avoid a public scandal. Hearst later joined Davies in Europe. Lake claimed she was born in a Catholic hospital outside of Paris between 1920 and 1923 (she was unsure of the precise date). Lake was then given to Davies' sister Rose, whose own child had died in infancy, and passed off as Rose and her husband George Van Cleve's daughter. Lake stated that Hearst paid for her schooling and both Davies and Hearst spent considerable time with her. Davies reportedly told Lake of her true parentage when she was 11 years old. Lake said Hearst confirmed that he was her father on her wedding day at age 17 where both Davies and Hearst gave her away.  Neither Davies nor Hearst ever publicly addressed the rumors during their lives. Upon news of the story, a spokesman for Hearst Castle only commented that, "It's a very old rumor and a rumor is all it ever was."

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On October 3, 1993, Lake died of complications from lung cancer in Indian Wells, California.