It is the first of a series of executions expected after the state Supreme Court overturned a lower court ruling blocking the use of a lethal injection.
Justices reversed the ban on the use of vecuronium bromide, one of the three drugs used by the state.
Lee's third request to stay the execution was denied.
He was pronounced dead at 23:56 local time on Thursday (0456 GMT on Friday) at the state's death chamber in its Cummins Unit prison, a Department of Corrections spokesman said.
Lee did not make a final statement. Instead of a last meal, he asked to receive communion, an official said.