Where in the book does it state Lyddie's age?

Different editions of the book will have slightly different page numbers. In my Puffin Books paperback edition, Lyddie's age can be found in the first full paragraph on page three. This is in chapter 1. It is the ninth paragraph of the first chapter. We are told that Lyddie is thirteen, and her brother, Charles, is only 10. Her sister Agnes is four, and her sister Rachel is six. Lyddie is the oldest of the children in the house, and already, in chapter 1, readers can see that Lyddie is a far more capable caregiver to the family than her mother is. It is Lyddie who protects the family from the curious bear. Lyddie's father is not present, because he left the family in search of gold, and he isn't likely to ever return.

The story begins one day in November 1843. From that day forth, 1843 will be known in Lyddie's household as the year of the bear. And in the very first scene we find out why: Lyddie is suddenly called upon to shoo away a bear sticking its head through the open door of their cabin. Lyddie has to take charge as she's the oldest among her siblings. We discover in the very first paragraph of the story that Agnes is four years old, and Rachel is six. It's not until page 3 of the book, while the bear's still wreaking havoc in the cabin, that we first find out just how old Lyddie is. She's thirteen years old, and her brother Charles in ten. That such a young girl could show such extraordinary bravery is truly remarkable, but is merely a foretaste of what's to come. Throughout the course of the book, Lyddie will face—and overcome—much bigger challenges than dealing with a curious, hungry bear.