Do you need to attempt to assassinate the president to go to Cuba?
Perhaps you.ve forgotten that Fidel Castro warned JFK that if the CIA attempted to assassinate him the JFK should watch his back.... Lee assumed that he could win acceptance into Cuba if it appeared as though he had tried to carry out Castro's threat...
Maybe, Oswald was a nut after all, but he was smart enough to know that his chances of reaching Cuba after attempting to assassinate JFK would effectively be zero. He didn't even own a car. Has limited funds. It would be a very silly plan to get into Cuba via attempting to assassinate the President when that entailed almost certain arrest or death before he could get out the Dallas. The only element that rings true here is that it does seem clear that in the months leading up to the assassination, Oswald's main objective was to create a resume for himself that might impress the Cubans into allowing him to gain entry to Cuba. Thus, the Fair Play for Cuba and arrest etc. It wouldn't surprise me if he made reference, even in a nonspecific way, to his attempt to kill Walker when he went to the Cuban embassy to impress upon them his commitment to the cause. But he was using the "normal" channels to reach Cuba. Maybe he was so nutty that he did envision himself perhaps somehow reaching Cuba after assassinating JFK and being given asylum as a type of revolutionary hero but he did seem to realize that the chances of getting away were extremely slim as demonstrated by his leaving his wedding ring and money with Marina.