Yes, governments are responsible for protecting their citizens from criminals, but are they allowed to lie to do that? Is it really ok to assassinate the accused with no trial, no witnesses, no evidence, no chance to present a defense? Even Jesus had a trial. Is that how anyone would want their government to treat them if they are accused of a crime?
I would also point out that the man is guilty of treason ONLY if you happen to believe Mohammed’s claims that he was told by some “angel” that it was ok to establish his Islamic dictatorship by force, and only if you are willing to overlook that while Mohammed established his dictatorship he repeatedly broke most of the 10 Commandments (killing, stealing, raping, adultery, etc.) Otherwise the guy was only trying to defend himself from the unjust aggression and oppression of Mohammed and his followers.
1753 A good intention (for example, that of helping one’s neighbor) does not make behavior that is intrinsically disordered, such as lying and calumny, good or just. The end does not justify the means. Thus the condemnation of an innocent person cannot be justified as a legitimate means of saving the nation. On the other hand, an added bad intention (such as vainglory) makes an act evil that, in and of itself, can be good (such as almsgiving).39
1756 It is therefore an error to judge the morality of human acts by considering only the intention that inspires them or the circumstances (environment, social pressure, duress or emergency, etc.) which supply their context. There are acts which, in and of themselves, independently of circumstances and intentions, are always gravely illicit by reason of their object; such as blasphemy and perjury, murder and adultery. One may not do evil so that good may result from it.
2482 "A lie consists in speaking a falsehood with the intention of deceiving."281 The Lord denounces lying as the work of the devil: "You are of your father the devil, . . . there is no truth in him. When he lies, he speaks according to his own nature, for he is a liar and the father of lies."282
2483 Lying is the most direct offense against the truth. To lie is to speak or act against the truth in order to lead someone into error. By injuring man’s relation to truth and to his neighbor, a lie offends against the fundamental relation of man and of his word to the Lord.
2484 The gravity of a lie is measured against the nature of the truth it deforms, the circumstances, the intentions of the one who lies, and the harm suffered by its victims. If a lie in itself only constitutes a venial sin, it becomes mortal when it does grave injury to the virtues of justice and charity.
2485 By its very nature, lying is to be condemned. It is a profanation of speech, whereas the purpose of speech is to communicate known truth to others. The deliberate intention of leading a neighbor into error by saying things contrary to the truth constitutes a failure in justice and charity. The culpability is greater when the intention of deceiving entails the risk of deadly consequences for those who are led astray.
2486 Since it violates the virtue of truthfulness, a lie does real violence to another. It affects his ability to know, which is a condition of every judgment and decision. It contains the seed of discord and all consequent evils. Lying is destructive of society; it undermines trust among men and tears apart the fabric of social relationships.
Catechism of the Catholic Church
Sirach 15:
[19] his eyes are on those who fear him,
and he knows every deed of man.
[20] He has not commanded any one to be ungodly,
and he has not given any one permission to sin.
Sirach 20:
[26] The disposition of a liar brings disgrace,
and his shame is ever with him.
Rev.21
[8] But as for cowardly, the faithless, the polluted, murderers, fornicators, sorcerers, idolaters, and all liars, their lot shall be in the lake that burns with fire and sulphur, which is the second death."
If Mohammed was so willing to lie to murder someone opposed to him, why should anyone believe he wasn’t willing to lie about his revelations as well?