I don't know the ethnic breakdown of Lvov between the wars. It may have had a sizable Jewish community as well as Poles and Ukrainians. It was on the Ukrainian side of the Curzon Line. At Yalta FDR tried to have it remain part of Poland (he was thinking in terms of keeping Polish-Americans voting for the Democratic Party) but Stalin refused and given the fact that the Red Army was there and we weren't, FDR had to give in.
I think the Holodomor was limited to areas under Soviet control.