Theory!
a) Mr Frazier and his sister Ms Linnie Mae Randle did see Mr Oswald with a long bag that morning
b) Mr Oswald did tell Mr Frazier it contained curtain rods
c) What was in the bag was not a rifle.
d) What was in the bag was two types of item.
This is simple:
Frazier - Oswald carried a long bag that was not his lunch. Oswald tells him it contains curtain rods. "I asked him where was his lunch and he said he was going to buy his lunch that day."
Oswald - tells the DPD he carried his lunch and not curtain rods (i.e. any long bag such as described by Frazier).
Put the statements together and the conclusion is that one or the other is lying. It is impossible to reconcile the statements and descriptions as Dishonest John pathetically tries. Frazier clearly and directly, with Oswald's confirmation, rules out that Oswald carried his lunch that morning. Any honest person with an ounce of intelligence would not suggest that a bag such as that described by Frazier was his ordinary "little" lunch sack. It's over two feet long! If there were even a scintilla of doubt, we also have Oswald's confirmation to Frazier that he is not carrying his lunch in the bag.
"I asked him where was his lunch and he said he was going to buy his lunch that day." Thus, who is lying and why? What incentive does Frazier, a dumb teenager, have to lie about whether Oswald carried his lunch or a long bag that morning? None. What incentive does Oswald have to lie about whether he carried a long bag? If it contained something exculpatory - like curtain rods - he has every incentive to tell the truth and admit that he did. If it contains something incriminating - like a rifle - he has every incentive to lie. What did he do? He lied. This is not rocket science unless you are dishonest - like Crooked John or biased. The facts and circumstances are crystal clear.