Judith Regan, the book publisher who was fired by the News Corporation last year, asserts in a lawsuit filed today that a senior executive at the media conglomerate encouraged her to mislead federal investigators about her relationship with Bernard B. Kerik during his bid to become homeland security secretary in late 2004. The lawsuit asserts that the News Corporation executive wanted to protect the presidential aspirations of former Mayor Rudolph W. Giuliani, Mr. Kerik’s mentor, who had appointed him New York City police commissioner and had recommended him for the federal post.