In a lengthy biography of LBJ, Robert Caro definitely makes mention of LBJ whipping it out and nicknaming his... Johnson. Caro is a highly regarded writer so he would fall under your need for a legitimate source.

I answered a related question awhile back. Here's a copypasta of the citation from Robert Caro's Master of the Senate, part of his multivolume biography of LBJ.

Even at college, where sexual boastfulness is a staple of campus existence, Lyndon Johnson's boastfulness -- and exhibitionism about his sexual prowess -- had been striking to his fellows. Exhibiting his penis to his roommates, Johnson called it "Jumbo"; returning to his room after a date, he would say "Jumbo had a real workout tonight" ... If he was urinating in a bathroom of the House Office Building and a colleague came in, Johnson, finishing, would sometimes turn to him with his penis in his hand. Without putting it back in his pants, he would begin a conversation, still holding it, "and shaking it, as if he was showing off," said one man with whom he did this. He asked another man, "Have you ever seen anything as big as this?"

http://books.google.com/books?id=wBE-34_KfcAC&q=penis#v=snippet&q=penis&f=false