Ellis has only recently become the gunman's lawyer, ahead of a coroner's inquiry.
In the memo, Ellis said the terrorist was having important documents withheld from him by the Department of Corrections, and the mosque shooter also believed his right to a fair trial was compromised.
Under Tarrant's instructions, Ellis said the shooter said his guilty pleas were obtained by "duress" and the conditions under which he pleaded needed to be taken into consideration.
Ellis said that it could be a breach of the Bill of Rights because he was "subject to inhumane or degrading treatment whilst on remand, which prevented a fair trial".
"He sent me about 15 pages of narrative of how he had been treated since he'd been in prison," Ellis said.
"He said because of how he was treated while he was awaiting trial and afterwards, [that affected] his will to carry on and he decided that the simplest way out was to plead guilty.
"By this, he means he was subject to inhuman or degrading treatment whilst on remand, which prevented a fair trial."
In the memo, Ellis also raised his lack of access to counsel, information and to documentation which would impact his ability to participate in the Coronial Inquiry.
"As he is held in virtually 24-hour solitary confinement in the Persons of Exceptional Risk Unit, there are issues arising as to his receiving information, and he has only limited access to daily news."
The Chief Coroner had written directly to the inmate, informing him of her decision to hold a Coronial Inquiry, but those letters were not passed on, Ellis said.
The attacker had also been sent two copies of the Royal Commission which were withheld from him by the department.
Without access to those documents, he advised his lawyer that he was unable to give detailed instructions ahead of any proceedings.
The memo also highlighted the Chief Coroner's failure to use the attacker's name in the Coroner's minute relating to the scope of the inquiry, only referring to him as "The Individual".
Ellis argued this was a "serious breach of human rights" and the "behaviour is deeply offensive, and unlawful" because he was no longer being treated as human.
"Tarrant is no longer a suspect, but a convicted criminal in detention; despite his horrific crimes that part of his legal life is over.
"He has been tried and sentenced and is entitled to be treated as a human."
Ellis said he was also entitled to be treated with respect and dignity despite his crimes, as stated in the Bill of Rights Act.
"It is not the least bit dignified, to be stripped of your name, it is an inherent part of your identity, and shows no respect for Mr Tarrant.
"It is very important that Mr Tarrant is not dehumanised especially by judicial officers."
Ellis said the Chief Coroner should apologise for the decision to name him only as the individual.
However, in a letter to Ellis, Judge Deborah Marshall said she did not agree that using that terminology was a "serious breach of human rights" nor was it relevant to the scope of the inquiry.
Ellis said he was aware of the major distress his right to appeal could cause on the victims' families and many parts of society.
"Nevertheless, carrying out client's instructions is every barrister's duty, and whilst this case is likely to be the pinnacle of professional difficulty, every accused or convicted person is entitled to exercise his right of access to the Court."
Tarrant's counsel and the Chief Coroner will meet next month.
Ellis said he had advised his client to appeal his sentence of life without the possibility of parole, because it is what is called a "sentence of no hope".
He said that was a breach of the Bill of Rights.
Ellis said he had spoken to the shooter about that and he was considering it.