It would be out of keeping with what I've learned about Lee's character, but it's possible he could have been nudged into doing it. It might have been easy to taunt him into doing it--"you think you're so tough" and all that. But again, I've never seen any persuasive evidence
Agreed. I used to consider it possible that the Cubans somehow prompted or encouraged Oswald to kill JFK, perhaps unintentionally, during his visit to their consulate in Mexico City. Maybe they said something like "So you want to be a hero of our Revolution, huh? Go take care of that warmonger JFK and
then we'll talk", never dreaming that Oswald could or would actually do it.
But even this just doesn't work. Neither Oswald nor the Cubans yet knew that JFK would ride right past the Depository in an open convertible a few months later. Oswald didn't even get his job at the Depository until after he returned from Mexico City and struck out at several other places, and then only by chance word of mouth.
Given the enormous hostility between the US and Cuba, much of which still remains, I am somewhat surprised that the Cubans helped our investigation as much as they did. Regardless of their role, they must have known how bad it looked for the man who killed the President of the United States to have visited their consulate in Mexico City only a few months previously. Even if they had only sarcastically suggested to Oswald that he assassinate JFK, I certainly wouldn't expect them to volunteer such information after the fact; to do so would have been probable suicide. I'd expect them to flatly deny that he had ever been there. I certainly wouldn't expect them to make Oswald's original visa applications available or to allow their consular workers to be interviewed.
All said, I still think it possible that Oswald had some sort of vague plan to return to Mexico City in triumph after the assassination, but that was purely the product of Oswald's deluded brain and not anyone in the Cuban consulate.