The 29-year-old journalist was shot dead in Creggan last Thursday night by dissident republican terror group the New IRA.
Three people – a 57-year-old woman and two teen males have been arrested over the murder but were later released unconditionally.
Responding to the reward offer, Detective Superintendent Jason Murphy of the PSNI’s Major Investigation Team said: “Lyra tragically lost her life when bullets were fired indiscriminately into the community in Creggan.
“It was a senseless murder of a gifted young woman and Lyra’s family and loved ones have been left devastated by their loss.
“I want to find the people who murdered Lyra and the information that can help us bring Lyra’s killer to justice lies within the local community.
“People saw the gunman – people know who is responsible. I’m asking them to come forward and help us.
“We have received widespread public support to date.
“And if this reward further encourages some individuals to come forward, this may help assist us in our efforts to get some justice for Lyra and her loved ones.”
The reward of up to £10,000 is available to anyone providing information directly to Crimestoppers charity which leads to the arrest and conviction of those responsible for Lyra’s murder.
The reward will only qualify if information is passed to Crimestoppers’ 0800 555 111 number or via the untraceable anonymous online form at www.crimestoppers-uk.org
Lyra was laid to rest at Carnmoney cemetery in Co Antrim on Wednesday following a funeral service at St Anne’s Cathedral in Belfast.It was revealed during the service that Lyra was planning to propose to her partner from Derry, Sara Canning, and wanted to have their wedding in Donegal.
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