The state's response detailed the killings that sent the men to death row and argued that justice has been denied to the victims' loved ones.
Lee, 51, who had long maintained his innocence in the 1993 murder of 26-year-old Debra Reese, also became the first inmate executed in Arkansas since 2005.
An hour after the murder, Jacksonville police arrested Ledell Lee in connection with Reese's murder after witnesses claimed they saw him walking down the street that Reese's house was on.
Arkansas had scheduled eight executions over an 11-day period before the end of April, when its supply of another lethal injection drug expires.
Lee's execution went ahead after the U.S. Supreme Court rejected last-minute appeals from his lawyers.
But the first three executions were cancelled because of court rulings.
Her family "had waited 24 years to see justice done", Arkansas Attorney General Deborah Rutledge said in a statement.
Two more inmates are set to die Monday, and one on April 27.
It takes five votes to get most things done at the court, including imposing or lifting a stay of execution.
Johnson and Lee are among a group of death-row inmates who have appealed to the U.S. Supreme Court to stay the executions, one of several legal battles being waged between the state and the inmates.
Legal experts said it was unlikely that the state could proceed with his execution.
The Arkansas Supreme Court also denied Thursday afternoon Attorney General Leslie Rutledge's request for reconsideration on the stay that was granted for Stacey Johnson.
In the ruling on the state's lethal injection drug, the Arkansas Supreme Court agreed with the state that it did nothing illegal in acquiring the muscle relaxant vecuronium bromide and lifted an order by a state circuit judge on Wednesday that blocked its use.
Gray said that drug, vecuronium bromide, "was essentially obtained illegally by the state", NPR member station KUAR's Jacob Kauffman told Morning Edition.
"Today is a shameful day for Arkansas, which is callously rushing the judicial process by treating human beings as though they have a sell-by date", the organization said in a statement.
Arkansas' attempt to carry out its first execution in almost 12 years wasn't thwarted by the type of liberal activist judge Republicans regularly bemoan here, but instead by a state Supreme Court that's been the focus of expensive campaigns by conservative groups to reshape the judiciary. Two pharmaceutical companies filed a court brief last week asking Baker to block Arkansas from using their drugs, but Baker did not rule on that issue.
The Supreme Court played a key role in Thursday's execution.
The Arkansas Supreme Court said in a 4-3 ruling that it would not reconsider its decision to stay Johnson's execution. The state can ask the Arkansas Supreme Court to reconsider its decision or appeal to the US Supreme Court.
Lawyers for the state said earlier this month that the prisoners know the state's supply of a key sedative expires April 30 and that it would be "impossible" to execute the prisoners because "Arkansas has no source of midazolam" beyond that already in stock. Prisons director Wendy Kelley has said the state has no way to obtain more midazolam or vecuronium bromide.
An eighth inmate, Jason McGehee, previously won a stay from a federal judge regarding his clemency schedule, and Arkansas has not appealed that ruling.