Supposedly he went there to get visa that would allow travel to the Soviet Union by way of Cuba.
LHO wasn't intending to go back to the Soviet Union. His intentions were to send Marina back there and for himself to stay in Cuba. (Ruth Paine's offer to take care of Marina & their kids temporarily solved that issue for him.) He prepared a resume to give to the Cubans to show his "credentials." Here are the notes he prepared while in New Orleans:
Page 1. https://www.maryferrell.org/showDoc.html?docId=1133#relPageId=361&tab=page
Page 2. https://www.maryferrell.org/showDoc.html?docId=1133#relPageId=362&tab=page
Page 3. https://www.maryferrell.org/showDoc.html?docId=1133#relPageId=363&tab=page
Page 4. https://www.maryferrell.org/showDoc.html?docId=1133#relPageId=364&tab=page
Page 5. https://www.maryferrell.org/showDoc.html?docId=1133#relPageId=365&tab=page
Page 6. https://www.maryferrell.org/showDoc.html?docId=1133#relPageId=366&tab=page
Page 7. https://www.maryferrell.org/showDoc.html?docId=1133#relPageId=367&tab=page
Page 8. https://www.maryferrell.org/showDoc.html?docId=1133#relPageId=368&tab=page
Page 9. https://www.maryferrell.org/showDoc.html?docId=1133#relPageId=369&tab=page
Page 10. https://www.maryferrell.org/showDoc.html?docId=1133#relPageId=370&tab=page
During interrogation on November 22, 1963, Oswald denied having visited Mexico City and I can find no plausible reason why he would lie about it, as it had nothing to do with the crimes of which he was accused.
Perhaps he realized that admitting visiting Mexico City would implicate his visit to the Cuban Consulate and he didn't want to tie the Cubans to the assassination. LHO reportedly not only denied it, but also got visibly upset (like he did when Hosty entered the interrogation) when his visit to Mexico City was brought up.
Yes, that's what I understand too. When he arrived in Mexico City he went directly to the Cuban consulate in search of a
transit visa not a regular visa: transit. He told Duran that his wife and family were going to the Soviet Union and he was going to join them. But he wanted to visit Cuba before returning and wanted a transit visa. Marina testified that he told her that he was going to go to Cuba and that she should go to the USSR. He then would (somehow) get them to come to Cuban once he was settled there.
When he was told by Duran that he needed to show a Soviet visa first before being given the Cuban transit visa he then went to the Soviet Embassy in search of one. According to the Soviets, he never actually filled out an application for one but asked them to expedite his previous request. And Soviet records indicate that they had made the decision earlier to turn down both Oswald's and Marina's requests for visas.
As to his denial: It's strange that supposedly he was framed for going to Mexico City by the FBI but then the FBI - Hosty - said he denied going there. That makes no sense. If they're framing him then why not say he admitted going there? He is dead; he cannot deny.
And if you believe Harry Holmes, the Dallas postal inspector who questioned Oswald on Sunday, Oswald admitted to him that he did visit Mexico City. I think Holmes' testimony here is very, very dubious.
Mr. BELIN. Did he admit that he went to Mexico?
Mr. HOLMES. Oh, yes.
Mr. BELIN. Did he say what community in Mexico he went to?
Mr. HOLMES. Mexico City.
Mr. BELIN. Did he say what he did while he was there?
Mr. HOLMES. He went to the Mexican consulate, I guess.
(Discussion off the record.)
Mr. BELIN. Now, with regard to this Mexican trip, did he say who he saw in Mexico?
Mr. HOLMES. Only that he went to the Mexican consulate or Embassy or something and wanted to get permission, or whatever it took to get to Cuba. They refused him and he became angry and he said he burst out of there, and I don't know. I don't recall now why he went into the business about how mad it made him.
He goes over to the Russian Embassy. He was already at the American. This was the Mexican--he wanted to go to Cuba.
Then he went to the Russian Embassy and he said, because he said then he wanted to go to Russia by way of Cuba, still trying to get to Cuba and try that angle and they refused and said, "Come back in 30 days," or something like that. And, he went out of there angry and disgusted.