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The National Enquirer, which is not know for stellar journalism, goes on to report that she has been pushing her voice hard in order to succeed as a singer like her more famous father Elvis.
In spite of what the story implies, although singing can lead to vocal cord damage (i.e., nodules)... singing in and of itself does not cause or lead to increased risk of cancer.
However, uncontrolled reflux which can cause throat and vocal cord damage CAN lead to throat cancer. In one report, reflux can increase the risk of throat cancer by 78% (this risk is separate from esophageal cancer).
WORLD EXCLUSIVE: LISA MARIE THROAT CANCER NIGHTMARE. National Enquirer 1/20/14.