My great grandfather was from outside L'viv, and almost as a little irony he is polish (and Poland was controlling l'viv at that time).
Not to make light of the situation, but the fact that you refer to l'viv as Ukraine (yes, I know we all agree it is) is a miniature proof that things do change and the way we look at things can be modified.
I mean, that was changed with massive forced relocations of the population (in both directions) by the Soviets.
It's not that the "people of Lviv" at the time stopped seeing themselves as Polish, it's that nearly the entire Polish population of the city was forced to relocate to Poland's post-war borders.
Not to make light of the situation, but the fact that you refer to l'viv as Ukraine (yes, I know we all agree it is) is a miniature proof that things do change and the way we look at things can be modified.