Why did the League not do more?
As a key member of the League, with a permanent seat on the council, Japan's promises that it had no ambitions in the region could not be ignored.
(needed a good relationship with Japan due to their own interests in far east + unwilling to challenge the Japanese)
USA not in league and also didn't want to take action.
Not doing anything also wasn't an option however, as smaller countries such as Finland demanded action.