Lipkin was born in New York, New York, United States and attended high school in Rochester, New York. He studied electrical technology at Cornell University, also attending physics courses by Hans Bethe and Bruno Rossi, and graduated in 1942. During the Second World War he worked as an engineer at the Massachusetts Institute of Technology Radiation Laboratory, developing a radar receiver. In 1950 he was awarded a doctoral degree from Princeton University, where he studied under David Bohm. Lipkin described his experiments as the first to show that positrons could be described by the Dirac equation.