Does it matter whether a victim of murder was a criminal or not?
The answer to this question must be prefaced by asking whether there exists a legitimate justice system or not.
If the law is legitimate and untainted by arbitrary favoritism, then execution is a possible sentence. In this case it is the law which executes the criminal, and the law stands above all individuals. Sometimes the sentence for a crime might be outlawry, in which case the law ceases to protect the individual's rights from encroachment by others, and such an individual may be "hunted down" and killed by an avenger, or else make an escape to a place of refuge.
I am concerned how this arguement synthesizes with "negative rights" arguements, so go ahead and shoot it down.
If there does not exist a legitimate seat of justice because either there are no courts (indifferent third parties) or because the courts are corrupted (by arbitrary laws or personal favoritism) then all is awash and chaotic. There is no justice. If I kill a murderer in order to avenge a lost loved one I stand in the face of whatever arbitrary justice exists. I may or may not be held accountable.
If there exists no legitimate seat of justice, there exists no legitimate authority to execute. (There should be no death penalty untill there is significant legal reform.)
Is assassination legitimate? Any powerholder will say no, because usually it is powerholders that are the target. The US treads a dangers path by pursuing the assassination of terrorists. If they think that they are safe from retaliation with this method of warfare they are ignorant and ought to look up the legend of Alamut
Assassination is a legitimate method of defensive warfare, and quite possibly the most humane. The question then arises, is this a defensive war?
Finally, as a Christian, killing is justified only in defense of "the least of these" and only when every lesser use of force has been expired. We believe that justice will be served on Judgement Day, and that our omniscient God is the only qualified arbitrator of this justice. Finally, we are not concerned for our own lives because we will be resurrected and we are not concerned for those we leave behind because God is a God of providence.