The Crown say the 33-year-old harmed the premature infant with injections of air into her feeding tube and bloodstream before she eventually died in the Countess of Chester Hospital's neo-natal unit in the early hours of October 23, 2015.
Letby denies murdering seven babies and attempting to murder 10 others at the unit on various dates between June 2015 and June 2016.
On Wednesday, jurors at Manchester Crown Court began to hear evidence about the nurse's ninth alleged victim, Child I, who was born at Liverpool Women's Hospital in August 2015 before she was later transferred to the Countess of Chester.
In a statement read to the court, Child I's mother said her daughter was about six weeks old when she thought she might be well enough to go home.
"I started to notice that she was looking different," she said. "She was looking around the room now, taking it all in.
"I was able to sit her on my knee. I remember looking at her and thinking 'We are going home'. She looked like a full-term baby, She didn't look frail or small."
The mother recalled that around this time she was allowed to bathe her daughter for the first time and that Letby helped prepare it.
She said: "I was so pleased to be able to bathe her. (Child I) was obviously enjoying it because she was smiling,
"Lucy even offered to take some photos using my mobile, which I agreed to.
"I didn't have too much to do with Lucy. She always appeared reserved compared to other nurses. She didn't really interact with parents."
The prosecution say Letby, originally from Hereford, went on to make her first attempt to kill Child I during a day shift on September 30.
She is said to have struck again during night shifts on October 12 and 13 before the baby's fatal collapse later that month.
Child I's mother said she was called at home in the early hours of October 23 and told she and her partner needed to go to the hospital immediately.
On their arrival she saw Letby with another nurse, Ashleigh Hudson, and consultant Dr John Gibbs.
She said: "They were working to try to resuscitate (Child I). I heard them all counting times.
"I asked Dr Gibbs how long had they been doing this, to which he said 20 minutes. I could see every time they were pumping her stats would go up, but when they stopped she flatlined every time.
"I remember thinking they can't keep doing it. I said to Dr Gibbs 'You can't do any more'."
After Child I was pronounced dead, her parents were moved to a private room at visiting time, she said.
Nurse Hudson and Letby asked her if she wanted to bathe Child I's body, she said, and that the girl's father initially declined before she agreed.
She said: "I didn't want to look back and regret not doing it so I said yes.
"Lucy brought the bath in. She said she could come in and take some photos which we could keep.
"While we were bathing her, Lucy came back in. She was smiling and kept going on about how she was present at the first bath and how (Child I) had loved it.
"I wished she would just stop talking. Eventually she realised and stopped. It was not something we wanted to hear.
"I remember it was Lucy who packaged up (Child I's) belongings to go home.
"Dr Gibbs mentioned about having an autopsy.
"I said I didn't want one because I wanted her leaving alone.
"He said I didn't have a say because her death was unexpected and the results would be needed to clear the hospital."
The trial continues.