How did the League of Nations play a part in causing the Second World War?
Rather than saying that the League of Nations helped to cause WWII, I would say that the League failed to prevent it.
The League was supposed to prevent wars by, among other things, providing collective security. If any nation atttacked another without just cause, the members of the League were supposed to help protect the nation that had been attacked. But then Japan sent its army to Manchuria. China appealed to the League for help. The League told Japan to leave but it refused. It called for economic sanctions but countries did not obey. Later, Italy invaded Ethiopia and essentially the same thing happened again.
This showed countries all over the world that the League could not stop aggressive countries or help countries that were being attacked. Seeing this, countries like Germany and Japan were not afraid of expanding further, thus causing the war to begin.