Windroll wrote:"No. But I stopped believing there was a power of good and a power of evil that were outside us. And I came to believe that good and evil are names for what people do, not for what they are. All we can say is that this is a good deed, because it helps someone, or that's an evil one, because it hurts them. People are too complicated to have simple labels."
Which Lyra replied with agreement.
So to answer the question, I don't think Mrs. Coulter "deserve" to die. Her action that caused her death at that moment was noble. For me, it's beyond "end justifies the means", or this character is evil at 80%, and that one is good at 40%. "people are too complicated to have simple labels".
Well said, Windroll! I am in complete agreement, with this point to add:
Nobody really "deserves" to die. No matter what they did, Life is too precious to be torn from someone as a punishment. Also, Coulter consigned herself to complete oblivion and pain when she threw herself into the Abyss. That's far worse than any death, and surely saving the world (albeit indirectly) more than makes up for any past crimes.
Mrs. Coulter is quite possibly the most complex character in the trilogy, and certainly the one with the most conflicting motives and commitments. Anyone should take a very close look at all of Coulter's actions and think very hard before judging her.
In the end, her love for Lyra and for Life win over her desire to dominate, and that is all that matters.