In a federal trial earlier this year, attorneys for 28 death row inmates argued the method could violate the amendment prohibiting cruel and unusual punishment.
Research shows the average time between sentencing and execution has increased by two-thirds in the past 20 years.
Lucio is scheduled to be executed for the death of her 2-year-old daughter. Her supporters say she was forced into a false "confession" and that new evidence exists that proves her innocence.
The ongoing project, entitled The Last Supper, featured prisoner's final meal requests, from a stuffed-crust meat lover's pizza to an apple pie to a Coke.
Former prosecutors and judges say Toforest Johnson's murder conviction was based on shaky evidence. The case is getting a new look as district attorneys review the integrity of past prosecutions.
Lisa Montgomery was scheduled to die by lethal injection on Tuesday, and would be the U.S. government's first execution of a female inmate in more than 67 years.
"Nearly three decades after [Dustin Lee] Honken coldly ended the lives of five people, including two young girls ... he has finally faced justice," a spokeswoman said in a statement.
In 2009, the state passed a law allowing inmates to challenge their sentence if race was a "significant factor." Nearly all inmates filed claims, but the law was later repealed and the cases voided.
Curtis Flowers was tried six times for the same crime, and the court said it made its decision because of bias in jury selection. Now it's up to Mississippi whether to try him again.
A divided court ruled against a Missouri man who said that because of a rare medical condition, death by lethal injection would constitute "cruel and unusual punishment."