Paula Abdul is going on the defense after Nigel Lythgoe exposed their text messages. In documents obtained by RadarOnline.com, Adul accused the 77-year-old television executive of launching a smear campaign against her, and she included a history of their private conversations that she claimed proved the sexual harassment she allegedly suffered from him. As this outlet reported, Abdul sued Lythgoe in December, accusing him of sexually assaulting her several times during her time as a judge on American Idol and So You Think You Can Dance. RadarOnline.com told you first — the Straight Up singer,…