Now!
Mr Oswald wanted to see JFK, but he didn't want to go out onto the steps and wait with all those co-workers there. He wasn't a mixer. Hated smalltalk. Wasn't much liked.
So he kept an ear and an eye out until it was obvious the motorcade was close to arriving, and then popped out.
It's very possible that Mr Lovelady
never noticed Mr Oswald's presence during the shooting. However, he
did notice the
apparent altercation between Mr Oswald, Officer Baker and Mr Truly by the front door shortly afterwards.
Here's what Mr James Jarman told the HSCA on 9/25/77:
"There was a Billy Lovelady standing on the steps.... Oswald was coming out the door and Lovelady said the police had stopped Oswald and sent him back in the building. Lovelady said that Mr. Truly told the policeman that Oswald was alright"If Mr Lovelady had not noticed Mr Oswald's presence just behind him during the shooting----------
------------then it would explain why he
misinterpreted the Baker-Oswald exchange as Mr Oswald being 'stopped' by the officer.
All Officer Baker wanted was someone to show him where the stairs were. Hence 'Do you work here?'
All of that later got transported up to the second-floor lunchroom and Mr Oswald's actual claims garbled beyond recognition.
Thankfully, though, this has turned up and it tells us what Mr Oswald really said!