I know it's a vague question but still I'm curious. Poland-Lithuania ceased to exist just 17 years before the war. Newly created Duchy of Warsaw fought on the side of Napoleon, many Poles and Lithuanians fought on Russian side (or so I assume). Did they fight each other? Did they have a problem with that?
It didn't happen much. Most Polish-Lithuanian soldiers at the beginning of the invasion tended to desert, and so they were moved to the Caucasus mountains to fight the Turks. It's worth remembering though that the vast majority of the people living in Poland and Russia didn't really identify themselves as Polish or Russians - national identity was in the process of being invented.