Shoot him in the act.
The plotters had hoped that Lee would be a stupid sucker that he would actually be behind that window where they could shoot him and kill him and then decorate a cop for being alert and catching the assassin in the act.
Then the headlines would have been: Assassin Shot Before He Could Escape....... Case closed
Lee knew that it would be very risky to play out his role as an attempt assassin behind that window..... so he adlibbed his role and merely left the spent shells and the hidden rifle and stayed out of sight until after JFK had passed by the TSBD.