On Tuesday, serving prisoner John Westland, 28, appeared before Leeds Magistrates' Court accused of Deane's murder.
The body of child killer Liam Deane was found in his cell at HMP Leeds on Sunday (12 November).
Westland will next appear at Leeds Crown Court on Thursday.
Police did not reveal any further details about the circumstances or the man who has died.
Tragic baby Luna had been left in the arms of Deane while her mother went to get some sleep on July 10.
Deane was imprisoned last month for the murder of his daughter, Luna, in July.
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But he lost his temper during the night when Luna continued to cry, Leeds Crown Court heard.
He admitted punching Luna to the face, squeezing her body and arms and shaking her.
"Luna suffered an assault at the hands of one of the people who was responsible for her care and wellbeing".
"He said he was responsible for all of the injuries that she had suffered and he said that Luna had not settled down and he lost control", added Michael Smith, the prosecutor during Deane's trial, according to The Sun.
Deane had been given a life sentence and was told he would serve a minimum of ten years in prison.
An ambulance was called after Deane had spoken to his mother, saying the baby was having difficulty breathing and had fallen and hit her head.
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He had shaken the two-day-old infant because she "would not stop crying", according to The Mirror.
Paramedics arrived and noticed her face was badly swollen and bruised.
Later, he admitted to the crime in a police interview.
Luna died in hospital three days after the brutal attack from "catastrophic brain injuries".
Mr Wright had read a victim statement to the court on behalf of Luna's mother. "I would not wish it upon my worst enemy".
"She was crying. You yourself were no doubt stressed and exhausted but you lost your temper".
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