Joan McKee has been in hospital for treatment for almost two weeks.
Her daughter Nichola Corner said the mobile, which holds many precious messages, went missing within the last week.
The Honor mobile was the last Christmas present Ms McKee bought for her mother before she was murdered nine months ago.
The 29-year-old journalist was shot in the head by New IRA dissident republican terrorists as she observed a riot in Derry’s Creggan estate on Thursday, April 18.
Despite being rushed from the scene to hospital by police, Lyra died in Altnagelvin Hospital from a single gunshot wound to the head.
The writer’s sister Nichola Corner said her mother drew comfort from reading messages Ms McKee had sent her.
“The phone has only sentimental value,” she said.
“My baby sister Lyra McKee bought it for our mom for Christmas 2018 – Lyra’s last Christmas. My mom often looked back on the many messages that Lyra sent her…but now she can’t.“Please help us find it.
“The phone had a hard case on the back with a little ring that she could put her finger through to make it easier to hold.
“If anyone finds this phone or knows of its whereabouts, please PM (private message) me or another family member. Thank you.”
Ms McKee’s sister-in-law Nicola made a similar appeal on Twitter.
“So many irreplaceable messages and memories please share and hopefully we can get this back #Lyramckee,” she wrote.
Despite a number of arrests by detectives, no one has yet been charged with the murder of Ms McKee.
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