Arkansas officials say such an order effectively blocks all the scheduled executions because they have been unable to get more of that drug, which is used as a paralytic as part of the state's three-drug lethal-injection procedure.
Up until Lee's final minutes, it was not certain that he would be executed.
The remaining four executions are still scheduled for next week, though more court challenges are expected.
Lee was convicted of murder and recently told the BBC he was innocent. He was put on death row for the 1993 death of his neighbor Debra Reese, whom he struck 36 times with a tire tool her husband had given her for protection.
Thursday saw a flurry of legal activity, with the new Supreme Court Justice Neil Gorsuch siding with conservatives in the 5-4 decision to reject the inmates' claim that the accelerated process amounted to "cruel and unusual punishment". It is hard to understand how the same government that uses DNA to prosecute crimes every day could execute Mr.
Lee was denied a stay Thursday in one of his bids to allow time for new DNA tests on evidence connected with his case.
Lee's attorneys had raced to court Thursday with a string of filings that raised various issues about Lee's trials and his representation over the years. During his first post-conviction hearing, his lawyer was drunk during the trial and interjected "blah, blah, blah" into his statements. With that ruling from the Supreme Court in place, Arkansas was prepared to proceed with Lee's execution. "Why these eight? Why now?"
The state originally set four double executions over an 11-day period in April.
"The governor knows the right thing was done tonight", said JR Davis, a spokesman for Arkansas governor Asa Hutchinson, who scheduled the multiple executions. The U.S. Supreme Court then delayed the execution for 10 minutes and later the appeals court halted it for another 45 minutes.
In a dissenting opinion, Justice Stephen Breyer said took issue with the state trying to use the drugs before their expiration date.
Earlier this month, the Arkansas Parole Board said that Lee's plea for clemency was "without merit", and on Tuesday, a judge declined to delay his execution. The state's supply will expire by the end of April.
The company, a unit of McKesson Corp, said it would not have sold the drug to the Arkansas prison system had it known it would be used in executions.
McKesson said it was disappointed with the court's ruling.
The state Supreme Court sided with state prosecutors and tossed out a restraining order that a county court on Wednesday night had placed on Arkansas's use of the paralytic vecuronium bromide - one of three drugs in the lethal injection cocktail.
Alito's stay was set to expire at 9:30 p.m. or by a subsequent order, whichever was later. Lee was pronounced dead at 11:56 p.m.
An Arkansas inmate who was executed late Thursday showed no apparent signs of suffering and lost consciousness quickly after the lethal injection began.
But Arkansas Attorney General Leslie Rutledge appealed the case to the state Supreme Court, which overruled Gray's decision, though it did not provide an opinion.
Her family "had waited 24 years to see justice done", Arkansas Attorney General Deborah Rutledge said in a statement.