Lwów is Polish spelling. It was called Lemberg when it was in the Austro-Hungarian Empire from 1772 to 1914. It's a city with very turbulent history. Under Austrian rule it was an important center of Polish and Jewish culture (but with German-speaking authorities). Lvov (Russian spelling Львов) was given to the Soviet Union, according to the Yalta conference agreements, and now its population is predominantly Ukrainian. Btw, Ukrainians call it Lviv (Львів)