Yes, LBJ and Helen Gahagan Douglas had an affair that lasted several years while they were in Congress. It was a pretty widely-known affair amongst politicians and the press, too. Robert Caro spends about a half-dozen pages in Master of the Senate detailing the relationship and wrote that LBJ and Douglas often arrived at the Capitol each morning in the same care.
It is often surprising to us that something like this affair wasn’t a bigger deal, but let’s not forget that the private lives and affairs of politicians simply weren’t reported on by the media in that era. FDR’s physical handicap and infidelity was no secret, yet most Americans had no idea that he couldn’t walk without assistance or that Eleanor lived in a separate house in Hyde Park. JFK’s many affairs weren’t public knowledge until after his assassination. LBJ also engaged in numerous affairs that the press was aware of, but none of them were reported on. It was just a different time.