You got it, although when he was born they called it Lemberg.
Our grandparents might well have been neighbors. I only met my grandparents a few times when I was young, but my mother told me that her father knew German, and one of the reasons he emigrated to the US was that his brother was drafted into the German army and wrote letters home telling him, whatever you do, don't let the German army get you. My mother explained that they came from a part of Europe that kept changing borders, the place was first in one country, then another, and they wound up in Ukraine. So he hopped a boat for Ellis Island.
He also had no problem understanding Yiddish, which is a German dialect anyway, because my mother told me when he went into a store with Jewish owners and undertook negotiations for something, he could understand what they were talking about to each other but never let them know. He got a lot of nice deals that way.
I think I have my grandfather's birth certificate among the papers here, I'll have to check.