Now it is part of the western Ukraine, on the Roztochchya Upland. It was founded in the mid-13th century by Prince Daniel Romanovich of Galicia, and historically been the chief centre of Galicia, that region that now separates Ukraine and Poland.
Its geographical position controls the east-west routes that pass across the Carpathians which is why so many have wanted it.
The Poles had in 1359. The Russians in 1648 and then Swedes in in 1704 thanks to Napoleon. A short-lived gov’t of the Western Ukrainian National Republic rose in Lviv in 1918, but the Poles drove Ukrainian troops out and regained control. Lviv was then seized by the Soviet Union in 1939 and, after German occupation, annexed by the Soviets in 1945. Yet in the end, Lviv returned as Ukraine’s cultural and spiritual center . It has a memorial of the city’s embattled past (WWII annexation by both the Germans and the Russians) embedded in a buttress of the Arch-cathedral Basilica of the Assumption of the Blessed Virgin Mary shown above.
Here’s a youtube of the interior and a service there.