Lil' Tyrant Dictator School is where Mr. Turner is sent after losing the big race in the 1970s.
It did not really appear but it is mentioned and a van from the school is shown taking young Dad Turner away. In the alternate time line, he is currently the leader of the world, a dictatorship where it is classified as rebellion if you don't always smile. He has a picture on his wall of him graduating from this school.
In the episode, "Father Time!", after Timmy accidentally melted his father's sports trophy with his heat vision and was punished for it, he decided to travel back in time using his Time Scooter to prevent his father from winning the trophy. After he succeeded in doing so, however, his father was sent to this school as a "reward" for coming in last. After returning to the present, Timmy saw that his father was alone, because he never met his future wife and never married her, never had children, and was dictator of the world (and forced everybody to smile or else). Timmy escaped and returned to 1970s Dimmsdale where he corrected the damage he caused to the timeline.