Lyda Mertz is nobody's fool, and nobody's damsel in distress. But that fact comes as a surprise—when we meet her, she seems like she's going have about as much backbone as a slug. However, by the end of Pure she's as kick-butt as the best of the other characters… and more assertive than most.
Lyda's character seems to serve a few different functions, but she's just as complex as anyone else. One reason we get her perspective during all of the shenanigans happening outside of the Dome is because we need to know what's actually happening inside the Dome. Lyda tends to be the kind of character that provides us with extra information; she finds out that people inside the Dome are planning a rebellion, and she gives us a glimpse into the Dome's unfair treatment of mental patients.
But what's going on when she stands up for herself in Ingership's house?
Lyda glances at Pressia then says calmly, "We'll do what we want." (59.19)
Get it, girl. Lyda is starting to emerge as a much more important character in the latter stages of the book. Not only that, but she's reinforcing the strength seen in many of the female characters. Lyda is duped by Partridge at the dance, put in a hospital, and manipulated by the government. But by the end of the book, she won't let anyone stand in her way, and we can guess that she'll play a pivotal role in the next book.
And let's not forget that Lyda deals the finishing blow on a Special Forces soldier (55.34). Didn't expect that out of just a regular schoolgirl, did you?