Rock was married to Anderson for four months in 2006, divorcing acrimoniously after four high-profile weddings and receptions around the world. Rock then got in a fight with Lee, another Anderson ex, at last month's MTV Music Video Awards in Las Vegas.
"You never want something to overshadow what your real talent is," said Rock, whose real name is Bob Ritchie. "When something starts to do that, you're kind of like, 'How do I lay low? I'm too busy having fun to lay low. I'm gonna sit in my house and not be seen? That's not any fun ...'"
"Rock N Roll Jesus," Rock's first set of new material in four years, include a swipe at Anderson via the country-flavored "Half Your Age."
Rock is in the midst of a theater tour to promote the album.
Notable deaths of 2014 [PHOTOS]
Polly Bergen, Emmy Award-winning actress, dies