OK, I think I can clarify this for you. Lemberg was a german language equivalent to Lviv (Ukrainian pronounciation) or Lvov (Russian pronounciation) In 19th century and until the end of WWI this city belonged to Poland which at the time was the subject of Russian Empire, after October Revolution in 1917 Poland managed to break away from Russia and establish an indepedant state until 1939, in September 1939 it was occupied by the Soviet Union as part of the Molotov-Ribbentrop Pact of 1938 which divided Poland between Nazi Germany and the Soviet Union, which in turn triggered WWII. When Germany attacked Soviet Union in June 1941 and occupied Lviv, it was again renamed to Lemberg, until 1944 when the city was "liberated" by the Soviets and was returned its original name Lviv/Lvov. In 1991 Ukraine gained independance and that is where it is located now. Historically speaking, this city was founded and built by ukrainians, but due to political turmoils, it for centuries remained the subject of different countries as most of Ukraine did.
If you need a present day location, look of the map of Ukraine (will be listed as Lviv), mid-late 20th century map of the Soviet Union (will be listed as Lvov), 19th-early 20th centuries maps of either Russian Empire or Poland (will be listed as either Lemberg or Lvov) Hope this helped.