She was born in Kaunas and studied at the local girls' gymnasium. After the Soviet occupation of Lithuania, the family was exiled in the first wave of deportations that took place in June 1941. Dalia's father was separated from the rest of the family and died in the Urals. Dalia, her mother, and her brother were first sent to the Altai region and then transported to Trofimovsk (), a prison island in the Lena River delta far beyond the Arctic Circle. Many of the deportees died of cold and starvation.