Lenzner was born in Manhattan, the son of Eleanor (Falk), a homemaker, and Joseph Lenzner, a dentist. His paternal grandparents were from Lithuania. He was raised in a secular Jewish family in Manhattan and attended Philips Exeter Academy. He graduated with a B.A. from Harvard University and with a J.D. from Harvard Law School. After school in 1964, following the advice of attorney Lloyd K. Garrison, he worked for the civil rights division of the Justice Department where he investigated the murders of three civil rights workers in Mississippi. He then worked as an assistant U.S. attorney under Bob Morgenthau in the organized crime unit in New York before becoming the director of the federal office of Legal Services in the Richard Nixon administration. In 1971, he served on a team under U.S. Attorney General Ramsey Clark that defended the Harrisburg Seven and in 1973, under Samuel Dash, as the chief counsel on the Senate Watergate Committee.