From the information I gathered about lateral thinking, it means to solve problems using unconventional means, sometimes even without using logic. Edward de Bono invented the L-game to illustrate lateral thinking. However, I fail to see how lateral thinking is used in solving the game. The L-game is essentially a very simplified version of Chess, both are strategy games and Chess is almost always the textbook example of logical games. In the analysis of the L-game, I found myself using purely logic (i.e. working backwards from the losing positions and identify which positions are "dangerous" etc). I do not see how "illogical means" could better help a player in winning the game. I might have misunderstood the meaning of lateral thinking, could anyone clarify?
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!).