Islam allows a court of law to administer capital punishment in two cases only, namely, intentional murder and spreading disorder in land (nuisance). Nowhere does the Holy Qur'an decree that people guilty of fornication be put to death. On the contrary, it prescribes the punishment of 100 stripes for the fornicators after the crime is proven in the court of law following the prescribed manner.
If the matter relates to a husband and wife, the Shari'ah ordaines the method of Li'aan. This shows that the Holy Qur'an leaves no room for honor killings. Moreover, Islam never allows individuals to take the law into their own hands and play with the lives of others. It is only the court which can decide what is to be done in a specific situation since all the directives pertaining to justice and society at large are addressed to the state.
From the individual perspective, there is an immediate need to look into reasons why an individual resorted to the undesirable means to gratify ones' desires. People usually do not commit mistakes but under the trance of physiological and psychological influences. A state is no doubt more concerned with the implementation of law and order. But an individual should be more concerned with the moral disposition of other people; he should strive to find out the reasons. In most ocassions it is the simple matrimonial arragement that will resolve the problem. In other cases, the concerned people may not be discharging their duties well toward each other, which leads to extra marital relations. Directing the consequence of one's own mistakes toward the other person is entirely absurd.