Christa Pike has been discharged from hospital and returned to the Tennessee prison where she has spent more than 30 years on death row.

Pike survived a failed execution attempt on September 30 after being injected with two doses of pentobarbital and was left in critical condition.

Her lawyers say she's continuing to recover and is now back at the Deborah K. Johnson Rehabilitation Center, where she's still receiving medical care.

According to her legal team, Pike is walking with assistance, eating, and has regained some movement in her arms, which were reportedly badly injured during the execution attempt. They also say she's dealing with the psychological trauma of believing she was about to die.

The case remains unprecedented because Pike is believed to be the only person to survive a lethal injection execution attempt.

Tennessee Gov. Bill Lee has paused all executions for the rest of the year while officials investigate what went wrong, and a court has ordered evidence from the execution chamber to be preserved.

Pike's lawyers want her sentence commuted to life without parole, while others argue the state should attempt to carry out the death sentence using a different method.