EXPLORATORY HYPOTHESISMr. Lovelady (as outlined in previous posts in this thread) did exactly what he told Mr. Bonnie Ray Williams he would do: he went back up to the sixth floor after picking up his lunch downstairs.
His lunch consisted of fried chicken and Dr. Pepper.
He first went to six, where he wasn't welcome.
He then went down to five, where he was not alone: one or two black employees were with him.
His & their presence was noticed by Mr. Arnold Rowland.
At some point, Mr. Lovelady decided to come back downstairs and watch the P. Parade from the front steps.
It was he who left behind the chicken bones & Dr. Pepper.This last detail became a MAJOR headache for the 'investigating' authorities, who became aware of the figure of a man in a red shirt in Hughes drinking from a bottle just as Pres. Kennedy is coming onto Elm. St.:

They needed this person to be Mr. Lovelady. They needed him NOT to have already consumed his lunch & soda upstairs. And so they decided that Mr. Lovelady's movements must narratively mimic those of Mr. Oswald.
Thus the following fake story was given him to tell:
After breaking for lunch, I went up to the second-floor lunchroom and bought a Coke, then I came downstairs and went into the domino room, then I went outside with my lunch & Coke to watch the P. ParadeAs for the chicken bones & Dr. Pepper bottle-----------Mr. Bonnie Ray Williams was made to take credit for them