Lyddie was facing society because the other girls in the mill were making fun of Lyddie when she first arrived, therefore she was in conflict with society. You can see this in the quote "Vermont, isn't it? said the one called Betsy,and a few of the others laughed" on page 56.
Lyddie was facing her mom as the other person in this situation. she was leaving but Lyddie did not want to and they were verbally fighting. You can see this on page 6. It says,"I cant stop you to go, Lyddie said, But I cant go with you. I cant leave the farm. When her mother opened her mouth to argue, Lyddie went on."
Lyddie is facing herself because she is mad at herself for not saying as much as she wanted to Charlie, therefore she is in conflict with herself. You can see this on page 31, "After he had gone, she thought of a hundred things she wished she had said...she longed to hear his laugh."