Nigel Lythgoe’s fourth accuser wants her identity to stay secret. Court documents obtained by RadarOnline.com reveal that one of his alleged victims, identified only as Jane Doe, is demanding her name and personal details remain private as she moves forward with the lawsuit she filed against the 77-year-old television mogul, who she claimed sexually abused her in 2018 at his Los Angeles home. Doe filed an order to seal portions of the complaint, informing the court she hopes to continue using the pseudonym in her back-and-forth battle with Lythgoe. The application was filed in Los Angeles Supe…