Lyra quickly comes to terms with the fact that Lord Asriel is her father, but she's confused about her emotions surrounding Mrs. Coulter being her mother. She doesn't worry long, however, as she throws herself into riling up the gyptian children and awing them with stories about Lord Asriel's unjust captivity. Outside of the fens, police search furiously for Lyra. She hears airships flying above, presumably looking for her, and either covers her blond hair or hides when she hears them. Lyra also asks Ma Costa questions about her babyhood until she creates a vivid, questionably truthful memory of what happened when Lord Asriel killed Mr. Coulter. When she's alone, Lyra pores over the alethiometer and tries to figure out how to read it. She discovers how to hold her mind so that the needle moves more purposefully.
The way that Lyra constructs a "memory" of Lord Asriel saving her from Mr. Coulter shows how at this point, Lyra is using a combination of truth and lies (she surely doesn't actually remember this) in order to come to a greater understanding of who she is and where she comes from. This play between truth and lie is, ultimately, what helps Lyra move toward adulthood. Relatedly, learning how to make the needle of the alethiometer move suggests that Lyra's own moral compass is sharpening.
On the third evening, the gyptians return to the Zaal. John Faa accepts gold and pledges of men from each of the six gyptian families. He thanks the assembly for their generosity, says that they'll charter a ship and sail north, and then invites questions. One man asks why the Gobblers are capturing children, and John Faa says that all they know is that it's "a theological matter." Another man says that because of Lyra, Parliament is considering rescinding the gyptians' right to free movement and asks why they're bothering to protect her. John Faa says that Lyra is Lord Asriel's daughter and reminds everyone that Lord Asriel fought hard for gyptian rights and has saved gyptian children from drowning. The man who asked the question sits, shamed into silence.
The implication here is that without Lord Asriel's advocacy, the gyptians wouldn't be in nearly as good of a position as they are now. This reinforces how vulnerable and marginalized the gyptians are as a group. While John Faa certainly can't answer every question truthfully like the alethiometer can, his insistence on doing the right thing, even when it's hard or could hurt the gyptians, provides Lyra another role model to look up to as she figures out right from wrong.
John Faa gives orders to the six family heads to begin preparations and asks again for questions. A man asks if John Faa intends to rescue Lord Asriel from the bears, but John Faa says that it'd be too costly. He will, however, look for information. Another woman asks if they plan to take revenge on the Gobblers for what they've done. John Faa says that it's more important to rescue the kids than it is to exact revenge, but when the time comes, they will punish the Gobblers. John Faa calls the meeting to a close. He and the other men head for a private room and Tony Costa laughs at Lyra when she suggests that they need her. When Lyra says she wants to go too, Tony promises to bring her back a walrus tooth.
Tony's promise to bring Lyra a walrus tusk mirrors Lord Asriel's promise to do the same. This makes it clear that to most adults, Lyra still looks like a child—and though she may be important, she's not someone they need to treat like an important adult. John Faa's focus on saving the children over exacting revenge demonstrates again that he's most interested in doing the right thing and supporting people.
Scowling, Lyra plays with her new friends. She eventually goes back to the Zaal and knocks on the door. When a man opens it, Lyra boldly says that she wants to come to rescue the kids and Roger, states all the things she knows, and suggests that they might need a child with them. John Faa tells Lyra kindly that they can't take her into danger and refuses, even when Lyra says that she's learning to read the alethiometer. He sends her away, and Lyra declares to Pan that they will go.
Lyra's request here is really a request to be accepted as an adult and let in on adult politics. Asking for this suggests that at least in some ways and on some levels, Lyra is ready to participate and grapple with more mature ideas.