I would agree that there was never any real evidence of a communist conspiracy. Over the years, the media has repeatedly run articles on the "Pedro Charles letters" as new evidence of such, but they were exposed as fakes many years ago, and are very old news. Johnson tried to suggest Cuban involvement at times, but there is no real evidence for this.
As for Lyndon Johnson, reports of his involvement have circulated ever since the assassination. Right-wing author J. Evetts Haley considered him responsible, as did left-wing playwright Barbara Garson, among others.
One theory has Johnson's own organization in Texas, using their hit man Mac Wallace, committing the assassination, or being involved in it. This has been revived recently, as noted below.
Another has Texas oil money behind it, with Johnson knowing ahead of time and helping to cover it up--this is what his mistress Madeleine Brown said.
A third has the Carlos Marcello organized crime family, which had a subordinate organization in Dallas, and which made payoffs to the Johnson organization through Jack Halfen, committing the crime and Johnson covering it up.
The latest theory, in Barr McClellan's book, and in the recently-suppressed History documentary, has a Johnson lawyer organzing the assassination, again using Mac Wallace in the plan.
At one point, Johnson's press secretary George Reedy, in a taped phone call, suggested that Johnson tell the truth about his Texas activities, with Johnson reponding that if he did that, he would go to jail. There were plenty of other activities, of course, to which this could refer, so it doesn't necessarily relate to the assassination.
Whether Johnson was involved remains a puzzle, but we seem to have more of the pieces than we once did.