Klein briefly joined the Communist Party during the 1940s, which led to trouble years later.

Klein was born in Omaha, Nebraska, the son of Blanche (née Monheit) and Leo Byron Klein. He went on to graduate from Los Angeles City College, where he learned calculus; the University of California, Berkeley, where he began his computer modeling and earned a B.A. in Economics in 1942; he earned his Ph.D. in Economics at the Massachusetts Institute of Technology (MIT) in 1944, where he was Paul Samuelson's first doctoral student.

In 1954, Klein's brief membership in the Communist Party was made public and he was denied tenure at the University of Michigan, in the wake of the McCarthy era. Klein moved to the University of Oxford, and developed an economic model of the United Kingdom known as the Oxford model with Sir James Ball. Additionally, at the Institute of Statistics Klein assisted with the creation of the British Savings Surveys, based upon the Michigan Surveys.

In 1958 Klein returned to the U.S. to join the Department of Economics at the University of Pennsylvania. In 1959 he was awarded the John Bates Clark Medal, one of the two most prestigious awards in the field of economics. In 1968 he became the Benjamin Franklin Professor of Economics and Finance at Penn.

Klein served as a thesis advisor for numerous well-known economists including E. Roy Weintraub in the late 1960s.

In 1969 Klein founded Wharton Econometric Forecasting Associates or WEFA (now IHS Global Insight), launching the econometric forecasting industry in the United States. Among his clients were General Electric Company, IBM, and Bethlehem Steel Corporation. He was the initiator of, and an active research leader in their LINK project, a consortium of model builders from many countries, which was also mentioned in his Nobel citation. The aim was to produce the world's first global economic model, linking Models of many of the world's countries so that the effect of changes in the economy of one country are reflected in the other. LINK, which is now operated by the United Nations, is still meeting regularly, most recently in October 2009 in Bangkok.

During the United States presidential election, 1976, Klein coordinated Jimmy Carter's economic task force. He declined an invitation to join Carter's administration. Klein has also been President of the Econometric Society. the International Atlantic Economic Society (1989–1990), and the American Economic Association (in 1977).

After formal retirement and until his death he was engaged in macro econometric model building high-frequency Models that project the economy in a monthly, quarterly frame. A publication on high frequency model containing countries such as US, China, Russia, India, Brazil, Mexico, Korea and Hong Kong was expected in 2008.

He died at his home on October 20, 2013. He was 93.