When he first took a step towards the murder with the intention of committing that murder

You say “without the need to delve into his mind”, but that is precisely the finder of fact’s role. For any crime with an intentionality element, the jury must “delve into his mind”; just as they would have to do if he had been arrested after the assassination — they would have to determine if he intended to kill the President by firing a rifle at him three times.

So until he squeezed the trigger he hadn't committed a crime?

No, he had committed a crime when a) he decided to murder the President and b) he had taken a concrete step towards fulfilling that intention. At that point he had committed attempted murder; once the President died, he had committed murder.

That is the law. At what point in the chain of events, the prosecution has enough evidence to convince a jury beyond reasonable doubt has a practical relevance, but many crimes are committed which can’t be proved every day. Different juries might be convinced at different points, and that’s fine — reasonable people can differ on the facts, but the law is what it is.

If a police officer has seen him with a rifle that morning, could he have (legally) stopped him?

Once the police officer had probable cause they could effect an arrest.

One definition of the standard derives from the U.S. Supreme Court decision in the case of Beck v. Ohio (1964), that probable cause exists when “at [the moment of arrest] the facts and circumstances within [the] knowledge [of the police], and of which they had reasonably trustworthy information, [are] sufficient to warrant a prudent [person] in believing that [a suspect] had committed or was committing an offense.”

Is it suspicious that Lee bough or owned a gun? No, lots of people do that. Is it suspicious that he concealed it in a bundle of curtain rods to bring it to his place of work which was right next to the route that the Presidential motorcade would pass? Probably. Is it suspicious that he set himself and the gun up in a window that was a perfect sniper’s nest to shoot at the said motorcade? Yes.

When he first took a step towards the murder with the intention of committing that murder

You say “without the need to delve into his mind”, but that is precisely the finder of fact’s role. For any crime with an intentionality element, the jury must “delve into his mind”; just as they would have to do if he had been arrested after the assassination — they would have to determine if he intended to kill the President by firing a rifle at him three times.

So until he squeezed the trigger he hadn't committed a crime?

No, he had committed a crime when a) he decided to murder the President and b) he had taken a concrete step towards fulfilling that intention. At that point he had committed attempted murder; once the President died, he had committed murder.

That is the law. At what point in the chain of events, the prosecution has enough evidence to convince a jury beyond reasonable doubt has a practical relevance, but many crimes are committed which can’t be proved every day. Different juries might be convinced at different points, and that’s fine — reasonable people can differ on the facts, but the law is what it is.

If a police officer has seen him with a rifle that morning, could he have (legally) stopped him?

Once the police officer had probable cause they could effect an arrest.

One definition of the standard derives from the U.S. Supreme Court decision in the case of Beck v. Ohio (1964), that probable cause exists when “at [the moment of arrest] the facts and circumstances within [the] knowledge [of the police], and of which they had reasonably trustworthy information, [are] sufficient to warrant a prudent [person] in believing that [a suspect] had committed or was committing an offense.”

Is it suspicious that Lee bough or owned a gun? No, lots of people do that. Is it suspicious that he concealed it in a bundle of curtain rods to bring it to his place of work which was right next to the route that the Presidential motorcade would pass? Probably. Is it suspicious that he set himself and the gun up in a window that was a perfect sniper’s nest to shoot at the said motorcade? Yes.