First of all, it is not the State that takes their right to life away, but the criminal, via their acts, give it up
When it is a question of the execution of a man condemned to death it is then reserved to the public power to deprive the condemned of the benefit of life, in expiation of his fault, when already, by his fault, he has dispossessed himself of the right to live."
Pope Pius XII
There is always the chance of repentance with a lost soul. Thank you!
The two are not mutually exclusive. For example, look at Timothy McVeigh. While raised Catholic, he had left the Church. While on death row, he had a reversion, and requested and received Sacramental Absolution.
He received the Sacraments again, including full Last Rites, just prior to his execution. So we will certainly encounter saint (small s) Timothy in Heaven.
Cardinal Avery Dulles noted this is his article on the death penalty
Capital punishment does not reintegrate the criminal into society; rather, it cuts off any possible rehabilitation. The sentence of death, however, can and sometimes does move the condemned person to repentance and conversion. There is a large body of Christian literature on the value of prayers and pastoral ministry for convicts on death row or on the scaffold. In cases where the criminal seems incapable of being reintegrated into human society, the death penalty may be a way of achieving the criminal’s reconciliation with God.