Yes, there is a method. But after that no new dialogue, and her brother react the same as normal when is she died.
There was at least one thread in the past where this was already discussed. So just a reminder:
There are many NPCs whose sole function is to die for the sake of dramaturgy. That's why there are no follow-up dialogues with these NPCs if you should somehow manage to save them, as they were never originally intended to live on.
