AHC: Lithuania sided with Poland in The Thirteen Years War

Which would not last 13 years in such case of course.
It is really not easy. Elites of Grand Duchy of Lithuania were more interested in further expansion into Ruthenian territory than in gaining mouth of main river of Lithuania and serious access to the Baltic. It was Poland's success that Lithuania remained neutral during this war (except for Samogitians, who blocked movement of Teutonic Order's troops from Livonia to Prussia), Lithuanian magnates considered joining the war against Poland to conquer Podolia, when Poland is busy fighting Teutonic knights.
So, how to change this situation? Perhaps Lithuania has strong ruler, who breaks power of magnates and decide to go to war against their will? This is tricky-last Grand Duke who ruled like tyrant (Žygimantas) was assassinated, there were also numerous attemps to assassinate Casimir later.
I wondered if it would be easier if Poland and Lithuania had separate monarchs at the time of war with the Order (say bishop Oleśnicki dies before 1440 and Vladislaus don't go to Hungary-he hestitated IOTL but Oleśnicki finally convinced him. But this option creates another problem-Vladislaus send Casimir to Vilnius as his governor, he didn't expected that his brother would take throne of GDL for himself, so instead of conflict with Teutonic Order there could be conflict between brothers instead-would Queen Mother convince her sons to find compromise? It was likely her idea that Casimir should take GDL throne for himself), but I'm still not sure it would work.
Any ideas?
 
I made a thread about this scenario earlier here.

What I'd imagine could suffice is Poland doing better in the Thirteen Years War, especially the later stages, so instead of seeing it as a futile effort to beat the Order, the Council of Lords would see it as Poland potentially taking over all of Prussia, and thus could join to prevent that by getting their own piece.

Getting some more early Vytautas nostalgia somehow would also help - Vytautas was one of the few rulers of Lithuania who actively tried to get Prussian territories and Klaipėda to be added to his country.
 
So Oleśnicki's early death should really help. Union with Hungary was his idea. As result Poland has to pay for Vladislaus' wars with Elizabeth of Luxembourg, which emptied Poland's treasure. Without this Hungarian adventure Poland would have more cash to pay mercenaries, thus war with Teutonic Knights would lead to quick Polish victory.
 
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