After studying in a school for pilots from 1937 to 1940, Lev Pavlovich entered Moscow's Institute of Aviation in 1940, but never completed his schooling there because of the German invasion of 1941. He was evacuated to the Siberian city of Irkutsk, where he worked until the end of World War II in an aviation plant as a technician.
In 1946, Lev Pavlovich entered Voronezh State University. He received his diploma in physics in 1948. He received his Doctor of Philosophy in physics in 1951. His doctoral thesis, written under the supervision of Maria A. Levitskaya, the first professor of physics at Voronezh State, was on gamma and beta processes in atomic nuclei.
Lev Pavlovich spent the remainder of his career in Voronezh State University's department of theoretical physics. He was an assistant professor (1952-1956), chair (1956-1993) and full professor (from 1971 until his death). During the reconstruction period following World War II, Lev Pavlovich taught nearly all the basic courses in theoretical physics and developed most of the department's elective courses.
Although Lev Pavlovich was apolitical, when decisions needed to be made, he took a democratic position.
Rapoport was intellectually inquisitive. His interests were not limited to physics or science. For example, Lev Pavlovich was quite knowledgeable about literature and the arts. Also, he typically devoted himself entirely to whatever he was doing, regardless of whether it was science or playing chess with his students.
Married Mariya Pavlovna Kolpachova, August 15, 1948 (divorced May, 1960).