Lee never did anything to arouse any suspicion, in either Officer Baker nor Mr Truly. Mr Truly can not explain what made him single out Lee. How did Mr Truly know that Dougherty, alone on an upper floor, wasn't the assassin or a co conspirator?
You are in denial. Of course Mr. Truly is going to focus on Oswald.
How could Mr. Truly know that Oswald (I see you are on a first name basis with the creep) did not do anything to arouse suspicion? Truly didn?t initially see Oswald as he was going up the stairs. Only Officer Baker did.
How does he know what Officer Baker saw after Mr. Truly started up the next flight of stairs?
All Mr. Truly knew is:
1. A rifle was found in the building, meaning one of his employees may have been the shooter.
2. Mr. Truly vouched for one of his employees who was being held at gunpoint by a police officer. For all Mr. Truly knew, he may have helped the assassin make his getaway.
And on top of that, Mr. Truly does not recall seeing Oswald after that. Naturally he is going to focus on Oswald until he can learn whether Oswald is still in the building or not. If Oswald is still there, he can focus on other employees. Or relax a bit and let the police handle it. But until then, he is going to do everything he can to compensate for a possible error in vouching for Oswald.