A Wild Justice: The Death and Resurrection of Capital Punishment in America by Evan J. Mandery  highlights LDF's role in the movement to end the death penalty. Mandery describes LDF as influential on "every major death penalty case in the United States" and "the leading voice in the abolition movement, dominating all others."
The book, which draws on primary source material, focuses on the work of LDF's former President and Director-Counsel, Jack Greenberg. Greenberg litigated Furman v. Georgia in 1972 in which the Supreme Court held that capital punishment, as it was then applied, violated the Eighth Amendment's "cruel and unusual punishment" clause, striking down the death penalty in Georgia.
The following is excerpted from the book, via Salon:
The National Association for the Advancement of Colored People Legal Defense Fund, sometimes known as the Inc. Fund or, more simply, LDF, had won countless legal victories since its founding twenty-three years earlier. LDF lawyers won Smith v. Allwright, a 1944 decision requiring Texas to allow African Americans to vote in primary elections. They prevailed in Morgan v. Virginia, the 1946 case desegregating interstate buses. They won cases protecting the rights of African Americans to serve on juries, striking down real estate contracts that precluded property sales to African Americans, and ensuring equal pay for black schoolteachers. And, of course, they won Brown.
In 1957, facing pressure from the IRS about LDF’s independence, Marshall broke LDF off from the NAACP. Thereafter the organization extended its already legendary reputation. In 1958 it protected the desegregation of Arkansas schools. In 1961 it won Holmes v. Danner, integrating the University of Georgia. In 1962 Bell and Motley won Meredith v. Fair, opening up the University of Mississippi. When Goldberg’s memorandum arrived in 1963, LDF’s lawyers were busy defending Martin Luther King, Jr., against contempt charges stemming from his protest of Birmingham segregation. Soon, thanks to LDF, the Supreme Court would dismiss all prosecutions stemming from the civil rights sit-ins.
Many people perceived the organization’s power as limitless. When the man who ran LDF’s primitive copying machine got into minor legal trouble, Greenberg offered to help. He replied, “Mr. Greenberg, I just want to get out of the fine, I don’t want to go to the Supreme Court.”
...The American criminal justice system was a complex scheme, with many variables at play, and courts generally didn’t allow statistical proof of discrimination. Despite the challenges, Meltsner and Clark felt that LDF should take on the issue. Even Heffron, generally the voice of restraint, felt they had nothing to lose. LDF received many requests from black defendants facing the death penalty. They generally accepted the cases even though capital cases are expensive to litigate, and LDF had limited resources. The lawyers simply found it impossible to say no. Heffron told his colleagues, “If we aren’t able to turn these cases away, we might as well focus on the real issue—capital punishment.”
Later the trio made their pitch to Jack Greenberg. Greenberg saw the complications of the issue, but nevertheless responded by appointing Heffron to study racial discrimination in rape sentencing. Whether this represented a change in LDF policy would later be the subject of some dispute. In his memoir Meltsner would write that at the time of this pivotal lunch, “capital punishment was not on the Fund’s agenda.” Greenberg would in turn disagree, saying that he had been considering a challenge to the death penalty for some time. Whether Greenberg or Meltsner is correct doesn’t matter much. From 1963 on, LDF influenced every major death penalty case in the United States and was the leading voice in the abolition movement, dominating all others."