That seems rather backwards... I even gave examples of murderers who might have more "sane" reasons to have murdered. Murdering your own kids is rather extreme and is something plenty of more "normal" murderers likely wouldn't contemplate doing.
I don't think that's backwards. The example you gave of revenge on someone who had wronged them is something that can randomly happen again, rather than killing your own children,. So the murderer in your example is a much greater threat to general society.
By the question wasn't about whether you think it is lenient or not the question is why even take the risk in the extreme cases?
Because if the point of life time incarceration is to protect the public [why take the risk?] and not just because she needs punishment, I'm questioning why, apart from emotive reasons, this murderer requires it rather than others.