The death penalty may be permissible when it is the only possible way to defend human lives. The Catechism of the Catholic Church explains:
Assuming that the guilty party’s identity and responsibility have been fully determined, the traditional teaching of the Church does not exclude recourse to the death penalty, if this is the only possible way of effectively defending human lives against the unjust aggressor.
If, however, non-lethal means are sufficient to defend and protect people’s safety from the aggressor, authority will limit itself to such means, as these are more in keeping with the concrete conditions of the common good and more in conformity with the dignity of the human person.
Today, in fact, as a consequence of the possibilities which the state has for effectively preventing crime, by rendering one who has committed an offense incapable of doing harm—without definitively taking away from him the possibility of redeeming himself—the cases in which the execution of the offender is an absolute necessity are very rare, if not practically nonexistent. (CCC 2267)