Oswald wasn't in the lunchroom.
Then please explain how he knew that Jarman and Norman walked past that lunchroom at 12:27. And if you still can't believe the facts, then please provide a plausible explanation how Lee could have known that there was nobody in that lunchroom who could have refuted his statement of "I was in the first floor lunchroom when the president past by the TSBD."
We have beat that one to death. Oswald had worked in the building for weeks. He had observed the typical patterns of his coworkers. For example, who had lunch where and with whom. It wouldn't take Nostradamus to figure this out. And, of course, a suspect does not obtain an alibi by claiming to see others. He obtains an alibi when others can confirm his presence. None did.
Lastly, I thought CTers questioned the accuracy of Oswald's statements while in custody? Does that only apply when he said something incriminatory? That's a rhetorical question since I know the answer.