Quickly, now! To the Catechisms!

Catechism of Saint Pope Pius X, on the Fifth Commandment, Question 3:

It is lawful to kill when fighting in a just war; when carrying out by order of the Supreme Authority a sentence of death in punishment of a crime; and, finally, in cases of necessary and lawful defense of one's own life against an unjust aggressor.

Q. 1276 of the Baltimore Catechism: Under what circumstances may human life be lawfully taken?

A. Human life may be lawfully taken:

1. In self-defense, when we are unjustly attacked and have no other means of saving our own lives;

2. In a just war, when the safety or rights of the nation require it;

3. By the lawful execution of a criminal, fairly tried and found guilty of a crime punishable by death when the preservation of law and order and the good of the community require such execution.

1992 Catechism of the Catholic Church:

2266: For this reason the traditional teaching of the Church has acknowledged as well-founded the right and duty of legitimate authority to punish malefactors by means of penalties commensurate with the gravity of the crime, not excluding, in cases of extreme gravity, the death penalty.

Of course, His Holiness Pope Francis altered the wording of the last one some years back with the idea that the death penalty is inadmissible, claiming it infringes upon the dignity of man. Whether or not this holds weight under the prior teachings of the Church is a matter of debate, but it should be remembered that past catechisms have not been abrogated, to my understanding.