Letby was convicted of murdering seven infants and attempting to murder seven others, but many continued to maintain her innocence
Guards at HMP Bronzefield, Surrey, have been told to check on her every hour over fears she could commit suicide or be attacked inside.
Inmates are said to be mocking the convicted child killer over the new film, including its opening scene which shows her being arrested and led away from her parents' house by police.
A source told The Sun: "They are keeping a really close eye on Letby because of the Netflix show. That means she is being checked on an hourly basis, or even more.
"Staff have also been told to engage in meaningful conversation with her and keep her talking for at least ten minutes at a time once a day or more. That is to gauge her mood and state of mind."
The newly released documentary shows Letby in bed as officers arrive to arrest her. Before going with the officers, Letby asks to see her cat, which she then hugs and kisses.
The footage shows Letby insisting her innocence to her parents, saying: "You know I didn't do it."
The 36-year-old, from Hereford, is serving 15 whole-life orders after she was convicted of murdering seven infants and attempting to murder seven others, with two attempts on one of her victims, between June 2015 and June 2016.
She continues to maintain her innocence.
The source added: "All the inmates are talking about the Netflix show and mocking Letby about it. Some have teased her about the opening scene, which shows her arrest.
Inmates cannot watch Netflix behind bars, but are in phone contact with people outside.
It comes after Former Detective Superintendent, Stuart Clifton, expressed his belief that the former neonatal nurse was innocent, a view supported by several high-profile figures since Letby's conviction in 2024.
Mr Clifton has been reviewing the evidence against Letby, who is set to die in prison after she was convicted of murdering seven babies and attempting to kill seven others at Countess of Chester Hospital.
Health Secretary Wes Streeting told LBC News on Wednesday that her fate should be a matter for the justice system and not campaigners.
Mr Streeting said: "Unless and until there is a judicial process that says that the court has got it wrong, I have to continue to have confidence in the court's judgments, and I'm certainly not going to provide a running commentary.
"I can see there's an active campaign on this, and there is a judicial process. If people think the courts have got it wrong, they can bring forward their evidence. They can test it and challenge it in the usual way."
The Criminal Cases Review Commission is considering evidence from a panel of doctors claiming natural causes and poor care caused the deaths.
Letby has been twice denied permission to appeal against her convictions in 2024. The Investigation of Lucy Letby was released globally on Netflix on Wednesday, February 4.
LBC has approached Sodexo, which runs Bronzefield, for comment.
