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Luckyj was born in 1919 in the village Yanchyn, today Ivanivka [uk], close to Lviv. His father was Ostap Luckyj, a Ukrainian modernist poet and member of the Polish Senate, and his mother was Irena Smal-Stotska, daughter of Stephan Smal-Stotsky, a Ukrainian philologist and Austrian parliament member.
After studying German literature at the University of Berlin, he fortunately went to England right before World War II for a summer program at Cambridge University. After the Soviet occupation of Western Ukraine, formerly Poland, in 1939, his father was taken by the NKVD and eventually died in a concentration camp. In 1943, Luckyj joined the British army and worked as a Russian interpreter in occupied Germany.
In 1947, he moved to Saskatoon, Canada for a position teaching English literature at the University of Saskatchewan. After two years he moved to New York to pursue a doctorate at Columbia University. His Ph.D. dissertation became the key Ukrainian literary scholarly text, Literary Politics in the Soviet Ukraine, 1917–1934. He participated in the activities of the Ukrainian Academy of Arts and Sciences, an important scholarly institution begun by Ukrainian émigrés in New York.
He became a professor at the University of Toronto and was involved in the creation of the Canadian Institute of Ukrainian Studies and Canadian Association of Slavists. His writing, both scholarly and of translation, was prodigious until his death in 2001.