I think you are just confusing two aspects of a character.
A Paladin of Lucinda holds one thing above all: The Protection of the Weave. That is it. That is the bottomline for this type of paladin. At the end of the day if the weave was served then he/she did their job.
Yet the question you are asking is considering an aspect of personality beyond duty. A Paladin of Lucinda is not bound by the codes and rules that a normal paladin is. Your Toran or Rofirenite is normally bound by a code whose first rule is to protect innocents and uphold the law. Now while a Paladin of Lucinda doesn't necessarily disrespects the law, their "lawfulness" comes from following the rules of being a Lucindite, thus if they ever have to break a human law to protect the weave it would not be considered against their character.
“Tolerate no harm to come to me or mine, my gifts freely given to those who follow used in defense of my body in The Weave and my Soul in the Coran arta i' Tha vair maen. For as surely as that which takes from life takes from me, that which takes from me takes from life.”[/i] – Fifth Coran arta i’ Tha vair
And then you have their Vows:
Lady of the Weave, I have heard your call and I will answer. I vow to be your servant and protect those who serve you. I shall defend Your Faith, Your Faithful and the Weave to the best of my abilities. I shall seek out those who corrupt the Weave and bring them to justice. I shall accompany and protect those who work in Your name. By my word, I am Yours.
See where I'm going? Nowhere there does it say "Protect the innocent". Its all about standing by a firm set of rules to protect Lucinda and their faithful. So while a paladin of Lucinda might truly have a good nature to assist an individual who is in need, shall it come between that and Weave, the second will always have priority.
Hope that helps somehow.