Lambrix was the second inmate put to death by the state since it restarted executions in August.
Before then, the state had stopped all executions for months after a Supreme Court ruling that found Florida's method of sentencing people to death was unconstitutional. In response, the state Legislature passed a new law requiring death sentences to have a unanimous jury vote.
Lambrix's attorney, William Hennis, argued in an appeal to the nation's high court that because his client's jury recommendations for death were not unanimous - the juries in his two trials voted 8-4 and 10-2 for death - they should be thrown out.
The Florida Supreme Court has ruled that Lambrix's case is too old to qualify for relief from the new sentencing system.
The US Supreme Court on Thursday night denied Lambrix's last-ditch appeal.
Lambrix was convicted of killing Clarence Moore and Aleisha Bryant in 1983 after a long night of partying in a small central Florida town, Labelle, about 50km northeast of Fort Meyers. Lambrix said he was innocent.
He and his roommate, Frances Smith, had met the victims at a bar, and returned to their trailer to eat spaghetti and continue the party, prosecutors said.
At some point after returning to the trailer, Lambrix asked Moore to go outside. He returned about 20 minutes later and asked Bryant to come out as well, according to Smith's testimony.
Smith testified at trial that Lambrix returned to the trailer alone after the killings, his clothes covered in blood. The two finished the spaghetti, buried the two bodies and then washed up, according to Smith's testimony cited in court documents.
Prosecutors said Lambrix choked Bryant, and used a tire iron to kill Moore. Investigators found the bodies, the tire iron and the bloody shirt.
Lambrix has claimed in previous appeals that it was Moore who killed Bryant, and that he killed Moore only in self-defense.
"It won't be an execution," he told reporters in an interview at the prison Tuesday, according to the Tampa Bay Times. "It's going to be an act of cold-blooded murder."
Lambrix's first trial ended in a hung jury. The jury in the second trial found him guilty of both murders, and a majority of jurors recommended death.
He was originally scheduled to be executed in 2016, but that was postponed after the US Supreme Court's ruling in a case called Hurst v Florida, which found Florida's system for sentencing people to death was unconstitutional because it gave too much power to judges, instead of juries.
Florida's Supreme Court has ruled that the new death sentencing system only applies to cases back to 2002.