Lil' Tyrant Dictator School is a school to train future dictators. Here is where Mr. Turner is sent after losing the big race in the 1970s.
All is knowh about this school is that has a van who transports the would-be dictators. In the alternate time line created by Timmy Turner, Mr. Turner is currently the leader of the world, a dictatorship where it is classified as rebellion if you don't always smile.
In the episode, "Father Time!", Timmy accidentally melted his father's sports trophy with his heat vision and was punished for it, so he decided to travel back in time using his Time Scooter to prevent his father from winning the trophy. He succeeded in doing so, however, his father was sent to the Lil' Tyrant Dictator School as a "reward" for coming in last. After returning to the present, Timmy saw that his father was alone, because he never met Mrs. Turner, 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.
In the alternate line created by Timmy Turner, the world was ruled by an alternate Reality Mr. Turner who was constantly smiling only to escape the harsh reality of his life.
The plot begins when Timmy Turner wished for heat vision in order to breeze through his chores, but wound up melting his father's prized trophy. This resulted in him being grounded and sent to his room by his infuriated father.
Instead of simply wishing to go back in time to prevent himself from melting the trophy, he decided to go all the way back to the 1970s to keep him from winning the trophy in the first place. Thus, Cosmo and Wanda wished up a Time Scooter for him that allowed him to travel through time. In the 1970s, Cosmo and Wanda were a young Bill Gates' godparents, and Timmy's Dad was training both to win the trophy and the young Mrs. Turner's love.
To ensure his father loses the race, Timmy embarked his young father on a regimen designed to leave him a wreck before the race, such as feeding him a constant supply of junk food and telling scary stories to him to keep him up all night. His effort succeed, as Mr. Turner did not win the trophy. However, Timmy then saw that the last place reward for this race (i.e. for his dad) was a scholarship to the Lil' Tyrant Dictator School. However, at this point, Timmy returned to the present day.
Upon returning to the present, Timmy saw that Dimmsdale had been turned into a totalitarian dystopia, where everyone was constantly smiling. Cosmo and Wanda was also no longer his godparents, since he no longer existed in this alternate reality, because Mr. Turner has never met his wife and never had a son. He met Chester and AJ, who did not recognize him, and tried to apture him. He managed to escape, and made his way to Mr. Turner's mansion.
Upon arriving there, Mr. Turner showed Timmy around, showing pictures of him graduating dictator college, then taking over the world, "with smiles", then showed a pedestal where he would put a trophy, before breaking his overly happy persona for a quick breakdown before resuming his normal happy persona*.
- NOTE: Scene in episode "Father Time!" when Alternate Mr. Turner freaked out over not having a trophy is currently a well-known internet meme. This meme is used by several internet users to show that coveted objects, people, or result of an unrealized action would be placed on a pedestal if these would be present.
When Timmy asked why he forced everyone to smile all the time, he said it to make sure that everyone was constantly happy as a way of not facing the reality of his life. When he revolted against this by saying that everyone cannot be happy all the time, "Dad" ordered him captured by Chester, AJ, and several guards. However, the 70s version of Cosmo and Wanda, who traveled with Timmy to this alternate present, distracted the captors by poofing up a lava lamp, leaving them entranced so that Timmy can escape. He used his Time Scooter to once again return to the 1970s.
Knowing that he had to make up for his error, Timmy tried to make sure his father could win the race. However, he decided to do this by posing as his dad and running the race for him. Immediately after the race started, Timmy realized that he was incredibly unathletic, but remembered he still had heat vision. He used this to melt the bottoms of all the other runner's shoes, stopping them and ensuring he wins the race. His mother declared his love for "Mr. Turner", where Timmy told her where to meet his actual dad, thus ensuring history is changed to normal.
Returning to the restored present, Timmy apologized for melting his dad's trophy. His father acceptted, giving Timmy the melted remains of the trophy. However, due to an offhand suggestion by present-day Cosmo. Bill Gates called the Internet the "Timmy", and as such, Timmy's name in this reality was "Internet".