How does the L-game by Edward de Bono demonstrate lateral thinking?
The idea is not to use lateral thinking to win the game, but to teach people to think laterally.

The L can be flipped and/or rotated as well as translated - why should you do a particular transform, and when. What move to make requires a certain amount of lateral thought.

Similarly in moving a neutral piece - not all the moves available are immediately obvious to a novice player - they must learn them.

By the time someone has mastered a few of the advanced moves, they are beginning to think laterally (at least that is the idea!).