The War ended when the Empire's second giant metal meatball was destroyed, which was silly because they should have realised that giant metal meatballs don't work when the first one was destroyed. The destruction of the second one cost the lives of both Sith Leaders, Sidious, who fell down a manhole, and Darth Vader, who defected to the jedi because his son, Luke Skywalker, needed help fixing his bike.
The Galactic Civil War, although not directly involving the League, is important to its history since it occured in the Galaxy Far Far Away which had not been influenced by the League since the fall of Darth Malak. The Galactic Empire had shunned the League and pretty much everyone had forgotten it even existed, even though Humans had migrated from the Milky Way to the Far Far Away Galaxy under League protection. The fall of the Empire and the Rise of the Rebellion into the New Republic (technically the New New Republic) led to a rekindling of the diplomatic relations between the two Galaxies and their governments.