Pike's lawyers filed an emergency motion on Friday to preserve "any and all evidence" related to her botched execution.
Hospital staff are working to save her life and clear the drug used, pentobarbital, from her system, the filing states.
During the execution attempt, prison officials tried to start intravenous (IV) lines by using at least seven needles on Pike, according to her lawyers.
At one point, Pike herself offered guidance of where they could try.
"One needle was bent in a 90-degree angle when it was removed," the filing states.
While receiving the two doses, "she could be heard crying, whimpering, and breathing loudly throughout the procedure", her lawyers said.
Tennessee Governor Bill Lee ordered an independent review into Pike's botched execution and he halted all executions in the state for the year.
The state's department of correction has defended the method it used, saying "the protocol does not allow for additional procedures beyond what was carried out".
Authorities are yet to say whether they will try again to execute Pike. They have not not offered any explanations about what went wrong.
Pike's attorneys previously warned that her conditions, including thrombocytosis (a blood-clotting condition) and small veins meant there was a risk she would experience "unnecessary" pain and suffering during a lethal injection.
In the latest filings, her lawyers allege that "at no point did any member of the execution team realise that the IV lines were not correctly placed or that the veins had blown and that the pentobarbital was, in whole or in part, entering Ms Pike's body".
They are requesting that all relevant physical, written and electronic evidence is preserved.
Dr Joel Zivot, an anaesthesiologist advising Pike's defence team, said two doses of pentobarbital was enough that "she would have surely died" had it entered her bloodstream in normal circulation.
The only possible explanation for her survival, Zivot said, "is that the pentobarbital blood level was never high enough to cause death" and that blisters on her arm after the botched execution indicated a ruptured vein.
So, instead of entering Pike's bloodstream, he said, the pentobarbital was more likely to have spread across the tissue under her skin.
Pike's medical condition of thrombocytosis may have also played a role, forming blood clots at the injection site that would potentially block pentobarbital from entering her veins.
Regarding the possibility the pentobarbital was degraded, Zivot explained that if this was the case, it could be due to factors including poor manufacturing or improper storage.