Born in Frankfurt am Main, Lipstein earned his Abitur from Goethe-Gymnasium in 1927. He enrolled at the University of Grenoble, and later finished his studies at the University of Berlin. He was of Jewish descent and emigrated to England in 1934. He earned his doctorate at Trinity College, Cambridge, in 1936.
During the war he spent some time in an internment camp as an enemy alien. His parents perished in the Theresienstadt concentration camp.
After the war he became a Fellow of Clare College and served as Professor of Comparative Law at the University of Cambridge from 1973 to 1976.
He was a renowned specialist in Roman law and conflict of laws within private international law and public international law and pioneer in comparative law.