When is murder justified by self-defense?

[Peh]

It is not justified if the attacker is fleeing or not being a threat to you while lying in pain on the floor or something similar.

It is justified if you killed him by accident while protecting your own life or someone else.
It is only justified if it is the only option you could do to defend yourself and the death of the attacker was not part of your will to kill him.

Obviously, it has to be analyzed from case to case.
If someone is walking towards you slowly with a knife, it is in my opinion not justified to just kill him. Because you have all the time to flee or while having a gun, to take your time and shoot him and make him incapable of hurting someone. If these options are not present at that given time, you can shoot him, but still your aim shouldn't be to kill him in the first place like most police officers do nowadays. They shoot to kill and not shoot to avoid more damage.

Again, you should never solve a situation by having the will to kill someone else in the first place. That's murder.

Oh and.. according to the thread title... murder is never justified. You should change it to kill, because to murder someone and to kill someone have 2 different intentions behind it and are not the same.