I don’t know that Johnson was an ideological Leftist, aside from being a murderer and crook, which is the essence of Leftism.
His thinking was more on the intellectual level of his famous statement about the Great Society: “We’ll have those n*ggers voting Democrat for the next 200 years.”
I don’t think Johnson himself was a Communist. A Communist would not have prosecuted the Vietnam war as he did. However, I DO think he made promises to the Leftists for cover. We can debate whether Oswald pulled the trigger or not, but I think he a weak link and was offered up by his fellow Leftists as the perfect patsy. In exchange, Johnson gave them much of what they wanted.
That’s my theory anyway.