LHO wrote the letter to the Russian Embassy saying he was there. But he lied to the investigators in DPD about it. This was just another one of LHO’s compulsive lies. His brother Robert said he despised LEOs and liked to try to show that he could “outsmart” them. I suspect LHO was just lying to mess with them, or at least to not cooperate with them.
Yes, one of the interesting parts of this matter is how he behaved, what he told the Soviets and Cubans, what he planned to do. If the Cubans give him that visa then he's gone, he's off to Havana to build a new life. How do the conspirators frame him then? All of their efforts are gone, he's in Cuba. How would they know he wouldn't be able to get that transit visa?
This is another example of the long list of things the so-called conspirators simply couldn't control, couldn't manage. From where Oswald was at the time of the shooting to this and everything in between, the ability of these conspirators was limited. In conspiracy world there simply seems to be no limits to what they could do: fake films and photos that fool experts 60 years later, order people to commit crimes and have them remain silent for the rest of their lives and on and on.
It's been more than half a century and over that time multiple generations of Americans in government and outside have looked into this tragedy. There's no there there. As Robert Oswald said, "Asking questions is good, it's right. But after the tenth time, the twentieth, enough already."