But Lucy covered the distance a dozen times a day...with that walk so peculiarly her own, like and irrepressible light-heartedness.
-- Narration (Book 1, Chapter 1)

Importance: This line of narration indicates the excitement and energy that Lucy has had since she was a child. This “irrepressible light-heartedness” is repeatedly shown to be a major facet of Lucy's character, as she is generally happy and optimistic. Throughout the novel, the story valorizes this trait of Lucy's.

How strange it was that James Mockford’s bad hip should bring about the most important thing that had ever happened to her!
-- Narration (Book 1, Chapter 5)

Importance: The construction of this narration seems to indicate a mode of free indirect discourse, meaning that the narration is actually conveying Lucy's inner thoughts and emotions. This line appears after Auerbach recommends Lucy to be Sebastian's new temporary accompanist. Lucy's excitement is evident and indicates her already growing admiration for Sebastian.

It was like reading his own...
-- Narration (Book 1, Chapter 11)