The structural problems of the League of Nations are often, unfairly in my opinion, blamed for the outbreak of the second world war, (whereas I'd say Germany and Japan were so hell-bent on war, no international organisation could have stopped them).
So how could we have it so that a stated aim of the War will be a re-establishment of the League of Nations, rather than starting from scratch with the United Nations?
This could just be in name only, or, ideally, as similar as possible to its pre-War form.
What would the Cold War be like with the UN replaced with a resurrected LoN?