Lange was born in Tomaszów Mazowiecki as son of the Protestant manufacturer Arthur Julius Lange and his wife Sophie Albertine Rosner. His ancestors had emigrated at the beginning of the 19th century from Germany to Poland. He studied law and economics at the University of Kraków, where he defended a doctoral dissertation in 1928 under Adam Krzyżanowski. From 1926 to 1927 Lange worked at the Ministry of Labor in Warsaw, and then was a research assistant at the University of Kraków (1927–31). He married Irene Oderfeld in 1932. In 1934, a Rockefeller Foundation fellowship brought him to England, from where he emigrated to the United States in 1937. Lange became a professor at the University of Chicago in 1938 and was naturalized as a U.S. citizen in 1943.