One has to distinguish between one's ethnicity and one's "citizenship" or which "country" ruled your family during its existence. One's ethnic background is determined primarily by family knowledge and traditional belief, but also by primary language, customs, practices, religion, etc. What "country" ruled in Europe over the past couple hundred years would have changed many times for most Europeans. So one might be an ethnic Pole in the 19th century, living in the Suwalki gubernia or province of the Russian Empire in a village that today is part of Lithuania. Or consider the French soldiers of Napoleon's army in 1812 who retreated so disastrously through lands now consider Lithuania but who remained to live, marry a Lithuanian woman and have children. Their descendants would, I'm sure consider themselves now ethnic Lithuanian, but perhaps there is some remnant of family history or in their name that illustrates that they have a French ancestor. But from 1812 to 1917, they all would have been subjects of the Czar of Russia, subjects of the Russian Empire.
So people always knew what ethnic background they were from, but they may not have know who ruled them. Most pre-WWI ethnic Lithuanian immigrants knew that they were Lithuanians and also that they were subjects of the Czar of Russia. But after Lithuania became an independent nation post-WWI, many of them would no longer say they were "Russian" subjects, but simply Lithuanian subjects because they were now proud to be from a nation that reflected their ethnic background as well as their new-found nationality.
By the way, there were ethnic Lithuanians who also spoke fluent Polish because they were influenced by Polish which was the language of most of the priests and major landowners in Czarist Russia lands occupied mostly by ethnic Lithuanians and they often lived among ethnic Poles, especially along border areas between the two ethnic groups. But they would know full well that they were ethnic Lithuanians, would speak Lithuanian in the family and among others, would live among other ethnic Lithuanians in America (at least at first), eat Lithuanian food, sing Lithuanian folk songs, etc.