Ironically, sexual harassment law in the United States might not exist in its present form without LBJ. Federal sexual harassment law grew out of Title VII of the Civil Rights Act of 1964, a law that LBJ was instrumental in passing. The actual reasons for sex discrimination being included within the law are complex, but suffice to say that the law was intended to combat racial discrimination and sex discrimination was included at the last minute. Some Senators backed the sex discrimination amendment because they thought it would kill the legislation and some legitimately believed in ending sex discrimination, but enforcement powers in the area were (and are) limited. The EEOC, the primary federal power behind that section of the law, doesn't have regulatory power (they can issue advisory opinions and join lawsuits). The first sexual discrimination case (Barnes v. Train) was still a decade after the passage of that law, and sexual discrimination as we know it today didn't really develop until the 1980s.

So, no one sued him because there was no grounds for a sexual harassment suit. But the lack of a lawsuit doesn't mean that his behavior didn't come back to haunt him. LBJ's major legislative accomplishments happened in his first two years as president, and by the end of his presidency he was battered by Vietnam, civil unrest, and scandal. Caro's books on Johnson make clear that many elected officials were bothered by Johnson's personal behavior but stuck with him because of his popularity and political power; once the popularity and power were gone, he lost the support of congressional powerbrokers.

Citation on one of these stories? I have never heard this and I was actually alive when LBJ was president.