Paula Abdulsent Nigel Lythgoe “adoring” emails and communication during and after the time she claimed he sexually assaulted her — and RadarOnline.com has the private messages. 74-year-old Lythgoe is using their private correspondence as alleged evidence in Abdul’s sexual assault lawsuit, in which she claimed he forced himself on her while she served as a judge on American Idol and So You Think You Can Dance. The TV mogul denied her allegations. “Lythgoe did not harass, bully, or sexually abuse Abdul. How do we know? Abdul’s own words: her private emails and public statements on social media, …