Lyrha and X'rhun save each others lives. Direct contrasts in many ways - they nonetheless find balance together. Both have a penchant for mischief that is all but unrivaled. 

It was not an easy road to get there. Like any reasonable, well-adjusted people, X'rhun and I'lyrha immediately distanced themselves when feelings first began to manifest, pretending the feelings growing between them were transient fantasies.

Though idealistic and passionate, X'rhun had far too much experience being robbed of the people he cared about, fighting for the losing side, and keeping friends only in passing. Lyrha should have been another temporary adventure: a maiden rescued from the brink of death, a pupil taught Red Magic, and gone on her own way. 

If she stayed, it meant letting her get to know the real him, beneath the Crimson coat. Having her by his side meant accepting the risk of losing a true comrade, again. After a lifetime of injustice, that might be too much a burden to bear.

Like X'rhun, Arya shows Lyrha that there are good people in the world, and that it's possible to change for the better. 

Initially it was an awkward relationship - Arya latched onto Lyrha quickly, and Lyrha was uncomfortable with the idea of being thrown into a protector's role for a girl who had been captured by pirate-slavers. But as both train in Red Magic under X'rhun, they find a shared ambition and passion to unite them, and a family where none had previously been before.

She calls Arya "Little Sister," a familial nickname representing just how important the other Red Mage is to Lyrha.