You could come up with a more creative way to handle the problem than concluding that murder is the only acceptable way to deal with a person who is causing problems.
Okay, let's go through the list;
A) Imprison enemy all forever where it cannot cause any harm to anyone
= Compassion check as imprisonment to all eternity is cruel punishment on anyone
. Deathlords do not age, they don't die nor they need eat nor drink. They do not die unless using charms or artifacts.
B) Forcibly redeem a person who seeks willingly cause harm and destruction in the world to achieve his goals (and I think most deathlords are willpower 8 and some even have conviction 5).
= Compassion check as breaking a will and forcing radical change upon someone is monstrously evil social-fu action in it's core even when it's done for good. As no matter of NMI can change deathlord from their motivation so you need UMI effects hammered on him.
C) Let his foe go freely and threaten with punishment if he does his actions again.
= Leads to go back square 1 and forces willpower burn each time a unredeemed deathlord strikes again (and he will and he seeks make you suffer greatly as revenge from humiliation it received) because your Compassion kicks you on the nuts being such a idiot in believing deathlord would learn it's lesson and take your threat seriously (or deathlord awaits until you die and then uses necromancy capture your ghost and make you his bitch, either way your screwed).
Any further ideas how solve the issue besides sending deathlord onto Lethe
? A Lethe which cleanses his soul from all negative memories, gives bliss and then erases all traces of personality from soul and sends it to new life which can be better than the one deathlord led? Your saying a compassion 5 Zenith priestess who works as ghost exorcists should roll compassion each time she sends ghosts to lethe who have no reason to linger behind (or linger because of negative influence and they inflict harm to the living)?
Sending ghosts to lethe is not murdering them as they had been already killed/died. Sending ghost to lethe is considered ultimate act of goodness and considering it's the anima power of Zenith may hint that Sol Invictus (who is paragon of compassion of the setting) considers the act holy and compassionate act (he would not had given Zeniths such power if he would consider it as act of cruelty). Destroying ghost (and the soul) with ghost-eating technique would call for compassion check (as it does not send soul to peace but purely vaporizes it out from existence).
However there is clear canon (if take Ink Monkeys as canon and the White Wolf has said they consider stuff from Ink Monkeys as canon even if they did not write it) reference that Sol Invictus can create ghosts from virtuous people by making them as righteous dead (they reside in Daystar). Some souls could be promoted to be unique heroic spirits (a kind to angels in the setting) from especially heroic souls which Sol Invictus paid attention to before
they died (also to consider; every solar is tied to go lethe directly and never become a ghost unless they made deals like deathlords did as their case is unique thanks Jade Prison situation). But it mentions if they fail their test to become one, they are send to Lethe so it means Sol Invictus himself considers the act going Lethe as divine blessing reward which comes at end of your life (before your reincarnated as a soul with no memories from last life).
So, god of virtue (which includes Compassion) more than one ways conveys his will and design that sending souls to lethe (or ghosts) is compassionate act.