LHO was a habitual liar. He lied about things even when there was no reason to lie. So I am not sure that he would have cleared up much if he had survived.
There's no reasonable argument that Lee Oswald did not lie....Nearly every human being does... And Lee was a trained espionage agent, whose very prerequisite is based on deception. However being a liar does not mean the person is a murderer.... And with regard to your statement that he had no reason to lie. You can't possible know whether Lee had good sound logical reason to lie about something. IMO the biggest liar of the case was J.C. Day, or Will Fritz....
I'm aware that many folks live in a fairy tale world where the good guys never lie and the bad guys are all liars.... Anybody who believes such nonsense should seek a psychiatrist .....