Lucy kept smiling and then hugged Billy. She probably was talking about Natalie's dad. While he was a man who didn't have much talent when it came to the skills of the tribe, he was straight like an arrow. So, naturally, he managed to pass through. Lucy's barrier that she put between herself and the others.
Apparently, Natalie didn't remember much of her father. He died when she was just six, after all. However, judging by Lucy's words, he could tell that Natalie was quite the daddy's girl.
"I am truly happy for you, Natalie," Lucy said. "We already said what we had to say to each other and we don't like to talk too much, but I will say that I am truly proud of you. You can easily take my place as the tribe's head, but you can achieve much more than that, so you don't need to. Do whatever you want and achieve many other things."
"Yes, Mom," Natalie said while also smiling like her mother.