Pangur Bán
Deconstructed
There's no reason they should be particularly close. The two were close in history for a period because after the Jadwiga marriage the Poles took their Lithuanian rulers hostage so to speak, but this wasn't inevitable and Lithuania's ties to Russia were usually stronger. Using the Poles to represent Lithuanians would be like using the Greeks to represent the Romans. The pagan Lithuanian empire is a real historic alternative worth the fun, Poland is really just one of several Germanized Slavic states.