Put yourself in LHO's shoes. He knows as soon as he takes the shot everyone working in the TSBD that day becomes an instant suspect. If he wanted to escape he would never have taken the shot from his place of work. That he makes it down to the second floor and is found seconds after the shooting sipping a coke is almost as good as an alibi but instead of hanging around with colleagues and answering any questions he leaves the scene, making himself a prime suspect. He also knows, prior to the shooting, that he will have to leave his weapon at the scene. He works at the TSBD but doesn't prepare a place to quickly stash the rifle and shells. Instead, knowing he is going to be questioned by police, he carries a false ID in his wallet connecting him to the rifle he knows is going to be found.
Escape plan? His plan should have been to get out of the building and get to Mexico, not go home, get a gun, kill a police officer then go to the cinema.
The guy was obviously a moron.