Princess Pony is a book that Lucy reads.
In "Sleuth or Consequences", Lucy is reading the book in the bathroom, so none of her siblings see her reading it. Lincoln comes into the bathroom however, making Lucy drop the book into the toilet, causing Lincoln to flush it, clogging the toilet. Lynn Sr. grounds everyone, until he finds out who clogged the toilet. Lincoln decides to find the culprit along with Lucy, unaware that she was the culprit.
Lincoln later discovers the Princess Pony book, and he and Lucy interrogate Lola, but she denies it. Clyde arrives at the front door and shows Lincoln a page that fell from the Princess Pony book, and a quote from the page is something that Lucy said earlier, making him confront her. She initially denies it until a Princess Pony poster is revealed, which makes her confess that she was the reader, and that she dropped the book in the toilet. She keeps it a secret from the rest of her sisters because she doesn't want to be teased for it. Lucy and Lincoln go to tell their sisters the truth, but Lincoln decides to claim the book as his, and takes the blame for clogging the toilet, resulting in everyone except him getting ungrounded. The girls state they'll make fun of Lincoln for the rest of his life for reading the book, but he is willing to take it, as he is not phased by their insults.
The complete title of the book is "Princess Pony: The Touching True Story Of A Delightful Pony Who Changes The World With Her Horse Sense".