The filing arrives just days after Abdul accused the former "American Idol" producer of sexually assaulting her on multiple occasions.
The celebrity judge claimed Lythgoe attempted to sexually assault her on more than one occasion and also groped her assistant.
"People that don’t need to win end up winning big time," Abdul said on Hudson's talk show.
Spectators lined up as balloon cartoon characters along with stars such as Paula Abdul and Mario Lopez made their way down New York streets on Thursday.
The singer got her moment with judges Paula Abdul, Simon Cowell and Randy Jackson at her Walk of Fame ceremony.
The entertainer returned to "Idol" as a fill-in judge for the live show and quickly caused a stir.
A face very familiar to longtime fans of the show will temporarily take the country singer's spot.
The singer, who's currently doing a Las Vegas residency, knows a good thing when she hears it.
From big hair to sequins to shoulder pads and bandage dresses, the singer, dancer and former "American Idol" judge has worn it all.
The former "American Idol" judge mesmerized audiences at the Billboard Music Awards with the midshow mishap.