Christa Pike has made a "profound" turnaround after last week's botched attempt to execute her in the US state of Tennessee, her lawyers say.

Pike, 50, was sentenced to death after murdering Colleen Slemmer with her then-boyfriend in 1995. She survived two injections of the drug pentobarbital on 30 September and was taken to hospital in a critical condition.

In a statement on Thursday, Pike's lawyers described her recovery as "remarkable" and said she is able to walk with assistance and is eating. She has also regained some movement in her arms, which were badly injured during the attempted execution, they said.

"Physicians are encouraged by her physical recovery," the statement said.

The case is now in uncharted territory as Pike is believed to be the only person to have survived an execution attempt by lethal injection.

"Christa is dealing with the profound psychological trauma of having survived a failed execution, including the terror, pain and uncertainty of believing she was about to die," her legal team said.

Pike's lawyers said they do not know the full emotional and psychological toll of the execution attempt or how long it will take her to recover.

They added that while she struggles to process what happened, she "continues to express concern for others, particularly the family of her victim Colleen Slemmer".

Slemmer's mother, who was among those pushing for Pike to be put to death, has branded the failed execution a "mess".

Pike's boyfriend at the time of Slemmer's murder, Tadaryl Shipp, was spared the death penalty because he was not legally an adult when the crime was committed. He remains in prison.

Pike was 18 and Shipp was 17 when they beat, tortured and killed 19-year-old Slemmer, whom they had met at a job training camp for low-income young people.

A court has ordered officials to preserve all evidence related to the failed execution, which could lay the groundwork for a future lawsuit against the state.

On Wednesday, Judge I'Ashea Myles ordered that "anything that was in the actual room needs to be preserved and maintained," including IV lines and syringes, as well as waste, such as packaging, inserts and labels.

The judge also demanded documentation on Pike's psychological condition before, during and after the failed execution.

She advised the state to take "special care" not to misplace or accidentally delete any information that may be pertinent to the case.

Tennessee Governor Bill Lee has ordered a pause on all executions for the rest of the year and said he wants answers about what went wrong.

Pike's lawyers have called on the governor to downgrade Pike's punishment to life in prison without parole.

Proponents of capital punishment have suggested using a different method to put her to death.