I don't doubt that Johnson was not as pure as the driven snow. In fact, just a few weeks ago I heard a repulsively treacly conversation between LBJ and Jackie Kennedy recorded after Nov. 22, 1963 in which Johnson's pathetic attempt at lighthearted flirtation sounded more like a dirty old man drooling over a hooker. But I would still need to see documentation, corroboration of some kind, that he seduced "students and interns" before I put stock in the word of a Clinton toady like Hamilton.
If it wiggled, LBJ would make a move on it. If it was cooperative, LBJ would bed it. He was not a picky man.
I don't know about "interns", per se, but "the age of consent" would've been a meaningless abstraction.
As you observed, LBJ could come across as a "dirty old man". Because that's what he was: a dirty old man...drunk with power.
Altogether, a disgusting human being -- who was an even more disastrous president, perhaps, than the First Felon.