Yes, Oswald was totally innocent. The reason he left work shortly after the assassination and went to him rooming house was because he wanted to retrieve his revolver and hunt down the dirty bastards who killed JFK. He even carried extra bullets in case there were more than a couple of assassins. Heck, maybe a whole bunch of 'em.
And like OJ Simpson looking for the killers on golf courses across America, Oswald knew that they were somewhere on the streets of Dallas.
But first, he wanted to see a movie.
And the rest is, as they say, history.