I know the challenge in the title is kind of my job, and I am definitely not looking for ideas, but I think it is interesting enough and different enough from my TL that all of you can have a shot. Plus, I don't think this challenge in particular was ever proposed, or at least I can't find one.
So. With a POD no earlier than 1240 AD (unification of the Lithuanian tribes into a single state by Mindaugas), make Lithuania as large and powerful as possible at 1900 AD. One major requirement, though - the state must not Ruthenize and basically turn into Ruthenia/Russia with a Lithuanian coat.