What Lovelady/Shelley "initial statements" are you referring to? I see they gave WC Testimony, but I am Not familiar with their "initial statements".
On the day of the assassination Shelley and Lovelady gave affidavits to the Dallas Police Department.
These are the initial statements they made regarding their activities around the time of the assassination.
By "initial" I mean that these are the very first official statements they made.
In his affidavit Shelley basically said that, after the shots he ran across the Elm Street Extension, met Gloria Calvery coming the other way, returned to the building and went inside to phone his wife.
In his affidavit Lovelady states that after the shooting he went back inside the building.
In their later lies both men insist that after the shooting they stood on the steps for around 3 minutes, spoke with Gloria Calvery, wandered across to the concrete spur that divides the Elm Streets, saw Truly and Baker outside the building, wandered down to the railroad yard where they stayed for a few minutes, then entered the building via the little known west door.
Both men forget to mention all this in their initial statements because what they actually did was as follows:
Both men were stood on the front steps when the shots were fired.
Shelley ran across the extension and bumped into a distraught Gloria Calvery who was screaming that the President had been shot. He ran back to the steps with her while she told Lovelady, and everyone else on the steps about the shooting. While this was happening Baker arrives and goes up the front steps into the lobby. Shelley, Lovelady and Truly go up the steps and enter the lobby. Shelley and Lovelady make their way to the back of the first floor while Baker is talking to Truly. Adams sees Shelley and Lovelady as she races to the back door. Seconds later Baker and Truly arrive on the scene where Baker sees the two white men who can only be Shelley and Lovelady.