The octogenarian had been convicted in 1991 on federal murder charges - and then again in 1996 on state charges - after mailing out four mail bombs in December of 1989.
"He believed the Democratic Party should be open and not be the party of George Wallace and the Dixiecrats", LaPierre said.
Moody became the oldest USA inmate put to death since executions resumed in the U.S.in the 1970s, according to the nonprofit Death Penalty Information Center.
Moody has maintained he did not send the bombs that killed Vance and Robinson. Moody, he added, fits the definition of a psychopath.
Prosecutors have claimed Moody delivered the bomb to this judge in anger that Moody felt derailed his livelihood and also delivered a second to the civil rights lawyer to confound investigators. "Moody not only committed capital murder, he also sought to interrupt the flow of justice". Moody was convicted in 1972 of possessing a pipe bomb - the Federal Bureau of Investigation said it detonated, injuring his wife - and was sentenced to three years in prison.
The US Supreme Court has temporarily delayed the planned execution of an 83-year-old convicted murderer in Alabama.
Instead, Moody's final efforts to avoid execution, which the US Supreme Court rejected, were largely procedural, including whether the federal government could turn him over to Alabama - and its execution chamber - while Moody served his federal sentence of seven life terms, plus 400 years. Moody had mailed two other bombs to the NAACP office in Jacksonville, Florida but they were intercepted and did not explode.
As his scheduled lethal injection neared, Moody sought to have it stayed, arguing against Alabama's ability to execute him because he was first sentenced on federal charges.
"He was a great judge, a great lawyer before that, and a great father", he said earlier as the execution loomed. In a recent letter to Mr Vance Jr, he wrote, "Had my Dad been murdered, I would want to know who had done it". The nation's high court had no comment on those last-minute appeals Thursday.
Moody's attorneys filed clemency petition to Alabama Gov. Kay Ivey, arguing that his age and vein condition would make lethal injection more hard.
"But he also made clear that as a judge, he has to follow what the law dictates and put aside his personal views, and he had to do that several times sitting as a judge", Mr Vance said of his father. "Tonight, Mr. Moody's appeals finally came to a rightful end". They say Moody, who had attended law school, sought to have his conviction vacated, so he "bribed an acquaintance to give sworn testimony that a fictitious individual used by Moody as an alternate suspect in his 1972 trial actually existed". "Justice has been served".