"Both the author and publisher find these claims ludicrous and highly amusing," I am told.
The show kept running for seven seasons from September 26, 2002 to May 19, 2009.
She was snapped with model David Gandy, said to be the highest paid male model in the industry.
A spokesperson for Lily declined to comment on the breakup, saying it was "a matter of privacy".
The pair had made a habit of meeting up in Europe for glamorous dates.
And there was even talk that marriage was a possibility.
When asked last year whether they would tie the knot, she replied: "I love him and he knows that and he loves me, so we'll see." Thirty-seven-year-old Enrique, who is of Cuban descent, is out of the picture now, though.