Regarding the debt of justice, there is no doubt that this is exactly what is involved. It is justice that justifies and validates punishment.
“A penalty is the reaction required by law and justice in response to a fault: penalty and fault are action and reaction. Order violated by a culpable act demands the reintegration and re-establishment of the disturbed equilibrium…" (Pius XII)
…the question, I suggest, is if this debt is ever such that justice demands the death penalty.
We know that justice demands a penalty with a severity commensurate with the severity of the crime (CCC 2266). We also know that the church has always accepted capital punishment as a just punishment for (at least) the crime of murder. (We either accept that or believe that the church has been acting and supporting what is unjust for 2000 years.) It seems, therefore, that capital punishment satisfies that requirement of a just punishment. This still doesn’t answer your question and distinguish between what may be applied and what should be applied.
Unlike other crimes whose severity can increase or decrease depending on circumstances, the severity of intentional murder is at a level where the death penalty is always commensurate (which is not to say it is always required). How, then, are we to decide when justice requires the application of such a penalty?
As far as commensurate severity goes, it is always just. The severity of murder cannot become less, the severity of the punishment cannot become more, it was just in the past so it is just today. There is always the question of whether the punishment is good for the society as a whole, but that is a situational issue which we can ignore for this discussion (even as we accept that it is a valid concern).
So: how do we decide whether it is mandatory or optional? I think an argument can be made that it is mandatory; I’m not sure an argument can be made that it is optional except on “harm to the common good” grounds, which we are (at the moment) ignoring.
On the mandatory side we have God’s rather explicit and uncomplicated command:
"Whoever sheds man’s blood, by man shall his blood be shed…" (Gn 9:6).
God then explains why he gave this command: “…for in the image of God He made man.” That is, the murderer forfeits his life because the crime he committed is so heinous. I think the Council of Trent echoed this in discussing the fifth commandment.
The necessity of explaining this Commandment is proved from the following. Immediately after the earth was overwhelmed in universal deluge, this was the first prohibition made by God to man. I will require the blood of your lives, He said, at the hand of every beast and at the hand of man.
In explaining the commandment Thou shall not kill, Trent states that “The just use of this power [to execute], far from involving the crime of murder, is an act of paramount obedience to this Commandment which prohibits murder.”
As I said somewhere up thread, we have lost our sense of the true outrage of murder.