Murder assumes the existence of a justice system. We don't know that any such thing exists. I don't doubt that Alice was going to kill her, or worse (That last panel is not the face of someone who could resist. Alice was already beating the helpless).
It's easy to say that X is not morally justified because Y might happen. But then Y happens, X is retroactively justified and Not X becomes the immoral action. It's all perspectives. You might stick to your guns, but that doesn't mean everyone will. Perspectives are academic except to the person what actually has to choose. That makes it easy to declare that This is not morally justified.
Alice didn't beat Ardent's sister down because she's a threat. She did it because she was angry. And because she seemed to enjoy it. But that doesn't change the fact that Ardent's sister is a weapon on mass destruction. Or the fact that she launched a large scale attack without any reasonable justification. (Trying to kill people and destroy their infrastructure--which amounts to a repetition in this instance--because they might know where that "rat" can be found is not morally justified.) Alice would be justified in construing LEJ's actions as an act of war.
The question, as yet unanswered, is whether Alice answers to a higher authority, or is the higher authority. In the later case, trials aren't relevant.
On a more personal level, the question of what is or isn't justified in this case IS the interesting point. Were LEJ a threat to Alice, Alice would be justified in killing her. Self defense. It all boils down the the perception of imminent danger If Alice believed she was in danger from LEJ, even now, lethal force would be justified. To a lesser extent, if Alice believed there was danger to others, she would also be justified. Legally, under most western law.
Morally? That's a moving target. But that's not fully relevant. Alice is NOT in danger. LEJ doesn't represent any kind of threat to Alice from what we've seen. To the extent that she represents a threat to others, as logn as Alice is near by, the threat is limited in scale. LEJ might kill one or two people before Alice could intervene, but it's unlikely she could introduce the same level of havoc as she'd created before Alice arrived.
So, one could argue that Alice doesn't have a moral justification to kill. If she does not, and someone else dies because she didn't, does Alice's moral uprightness justify that death? How much ar Alice's town, her people, her rectitude worth? Is she willing to trade one for the other two? What might happen because of that trade is an unknown, but the moment she chooses, she betting one for the others. She could make the "Moral" choice, avoid stains, and hang the town and the people in the balance.
Or she can get dirty and ensure the safety of the innocent. Depending on what element you consider more important (lives or morals) you can frame any choice Alice makes as the wrong choice. Not just incorrect, but morally lacking.
I still don't think Alice is going to kill anyone today. But the WHY has the potential to be interesting.