This is going to sound absurd, and it probably is, but hear me out. What if Lee H. Oswald isn't actually a person? He started as a person and became a brand. As the plot to assassinate Kennedy developed and started to depend on Lee being involved, fake Oswalds started getting planted to confuse and distract and whatnot. At the point I'm at, about halfway through In Dallas, Lee has a normal, boring job and Marina is doing normal wifey things like hanging out with other wives or whatever. So the plot continues to develop and they get less dependent on Lee because now they have all these fake Lees to carry out whatever needs carrying out in accordance to the plan. The original Lee Harvey Oswald is left to his humdrum life, and fake Lees start getting trained in shooting, if they weren't already proficient. This means that any one of the copies could have be the assassin. This also makes sense since Lee still wasn't entirely on board with assassinating Kennedy.
So yeah I'm probably extremely off-target because I haven't finished the book yet, but it's a nice little AU to consider. Thoughts?