All kinds of problems here. First of all, Oswald could not have gotten from the sixth floor sniper's nest to the second floor lunchroom in time to be seen by Officer Baker. As historian David Wrone has often pointed out, the WC found it necessary to severely rig the reenactment of Oswald's alleged movements in order to appear to get him to the lunchroom in time to be seen by Baker. Wrone discusses this point in detail in this lecture:
Second, there were people on the stairs who would have seen Oswald if he had come down the stairs. We know he could not have used the elevator. He would have had to come down the stairs.
Third, a huge problem with the WC's account is that if Oswald was only one foot past the foyer door when Baker spotted him, as Baker belatedly claimed, then Roy Truly, who was running ahead of Baker, surely would have seen Oswald either coming off the stairs, or walking across the landing toward the door, or opening the door. The Commission itself admitted that Oswald must have gone through the foyer door only "a second or two" before being spotted by Baker:
Since the vestibule [foyer] door is only a few feet from the lunchroom door, the man [Oswald] must have entered the vestibule door only a second or two before Baker arrived at the top of the stairwell. Yet he must have entered the vestibule door before Truly reached the top of the stairwell [leading to the second-floor landing], since Truly did not see him. (WCR 151)
But the Commission never explained how Oswald could have done this. If Oswald had gone through the foyer door before Truly reached the top of the stairs, he would have been several feet beyond the door by the time Baker reached the landing, and thus would not have been visible to Baker through the window. And, if Oswald had entered the door "only a second or two" before Baker reached the top of the stairwell, then Truly could not have missed seeing him. Nor did the Commission explain how Baker could have been the least bit unsure about whether or not Oswald had gone through the foyer door if Baker spotted Oswald right next to the door and if the door was in any kind of motion at the time. I discuss this issue in detail in "The Baker-Oswald Encounter: Proof that Oswald Did Not Shoot JFK?" and in "Where Was Oswald During the Shooting?":
https://miketgriffith.com/files/bakerlho.htmhttps://miketgriffith.com/files/wherewasoswald.htmAbout three months before the assassination, U.S. intelligence officer Richard Case Nagell warned Oswald that he was being set up as the patsy for Kennedy's murder, but Oswald dismissed his warning. This could explain why Oswald did nothing to prevent himself from being framed. Or, as some have suggested, he could have been led to believe that Kennedy was not the target but that Connally or LBJ was and that his role would be harmless or non-existent, or that the shooting would merely involve firing misses near the motorcade to alert Kennedy that his security arrangements were very lax.
Oswald was clearly supposed to meet someone at the Texas Theater. I suspect that it was only after he was arrested that he realized he had been set up. He might have realized this earlier, but if he did, I find it curious that still went to his meeting at the theater. In any case, once he was in police custody, he fully understood that he had been set up, which is why he uttered the famous and revealing statement "I'm just a patsy" after he was in police custody, and why he told his brother Robert not to believe the "so-called evidence" against him.
Finally, a voice stress analysis/psychological stress evaluator polygraph was performed on Oswald's statement that he didn't shoot anyone, and the results indicated he was telling the truth. David Scheim discusses this in his book
Contract on America: The Mafia Murder of President John F. Kennedy. Here is George O'Toole's original article on the PSE test on Oswald's statement:
http://jfk.hood.edu/Collection/Weisberg%20Subject%20Index%20Files/O%20Disk/O%27Toole%20George/Item%2021.pdf