Rodney was born in Manhattan, New York, the third of four children of Isabel Cotton and Max Rodney. The Rodneys moved from the Bronx to Brooklyn when Lester was 6, where his lifelong love of the Dodgers developed. Rodney’s father lost his business, and then the family home, in the 1929 stock market crash that began the Great Depression, an era in which Communism and other radical social philosophies captured the attention of the intelligentsia. Rodney earned a partial track scholarship to Syracuse University, but his family could not afford the other half of his tuition so he did not complete his formal education. To supplement the family income, he took odd jobs, including helping his attorney brother-in-law and chauffeuring rich children to school.

Rodney's favorite jobs though involved sports, and in 1936 he parlayed his high school background in sportswriting into a job with the Daily Worker and its Sunday edition, the Sunday Worker, the party organ of the Communist Party USA, or CPUSA. There Rodney was able to combine sports journalism with his developing sense of social justice, to champion social issues, most notably the desegregation of major league baseball. Many American Jews felt as persecuted as African Americans, and it was not a stretch for a young Jewish intellectual to see the contradiction of the fight against Hitler's bigotry and the continued oppression of black people in the United States. Rodney was given wide discretion in his sportswriting, permitted to criticize baseball, America, and Hitler in order to prove his point that some African American ballplayers were equal to white major leaguers. He leveled much of this criticism at Branch Rickey, the general manager of his beloved Dodgers.

Rodney served in the South Pacific in World War II, and it was during his service that Branch Rickey announced the signing of Los Angeles native and war veteran Jackie Robinson to a minor league contract. Rodney's paper had touted Robinson’s abilities for nine long years leading up to this event, and Daily Worker editor Mike Gold wrote an editorial praising Rodney’s efforts as bringing desegregation to fruition. Rodney was one of the few white sportswriters of his time to devote a great deal of space and praise to black athletes. His sports page often carried more stories about Joe Louis and Kenny Washington than on those white athletes whose prowess was the subject of the mainstream papers. Rodney's outspoken commentary often publicly pitted him against other sportswriters, but they would often offer information for Rodney to publish that they could not themselves use. Soon after returning from the war, Rodney met the woman who would become his second wife, Clare, a lifelong educator, and they were married on April 21, 1946. Rodney stayed with the Daily Worker until the mid-1950s, keeping on top of racial issues in sports.

Following Nikita Khrushchev's 1956 Secret Speech detailing the crimes of the Stalin era, Rodney joined Daily Worker editor John Gates in an attempt to open the pages of the paper to debate. CPUSA leaders suppressed this staff revolt, and suspended publication of the paper as a daily. After 22 years as the Daily Worker's sports writer, Rodney resigned from the CPUSA and the paper in January 1958 to seek a new life in California. The Rodneys moved from New York to Torrance, California, in 1958, where they lived for 31 years. Rodney continued to work as a journalist, most notably as the Religion editor of the Long-Beach Press Telegram. The Rodneys had two children, Amy and Ray, and later a granddaughter, Jessie. Rodney kept active all his life playing sports, and in his 60s saw success in his senior amateur tennis career, ranking as the #1 or #2 player in his age group in California until retiring from competition in 1998. In 1990, the Rodneys moved again, this time to Walnut Creek, California. Clare died in May 2004.

Rodney celebrated his 96th birthday on April 17, 2007 in Walnut Creek, California with his partner, Mary Reynolds Harvey. Rodney died on December 20, 2009.