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It was six years ago when Lucy, would have celebrated her 28th birthday this year, was shot dead at her home in Walton.
In the early hours of 3 August 2005, three men burst into her home on Lambourne Road, Walton, they shot Lucy, as she lay on the sofa downstairs. Lucy's partner Gary and their two-year old daughter were sleep upstairs.
Even as a toddler was heard crying upstairs, the offenders poured petrol around the living room and set fire to the house.
Detectives believe the offenders would have been in no doubt they were killing a young woman, with police saying they could have claimed the lives of two more people that night had Gary not escaped the flames by jumping, with his daughter in his arms, from an upstairs window.
Detective Superintendent Ian Mulcahey said: "Six years on and we are determined as ever to find justice for Lucy and her family.
"Lucy was an innocent victim and her death has not only robbed her three children of a mother, but also her parents of a loving daughter.
"We believe that someone, somewhere knows what has happened to Lucy and I hope that the passing of time will enable people to search their consciences and find the courage to come forward.
"It's never too late, any information we are given will be acted upon."
Police are hunting for Kevin Thomas Parle, 31, in connection with the murder of Lucy Hargreaves as well as Liam Kelly.
Parle is described as white, 6ft 5in tall with a broad build. He has blue eyes, cropped ginger hair and a 1"scar on the left side of his head.
It's possible that Mr Parle is living abroad (Spain) and there are two European arrest warrants out for arrest.
16-year-old Liam Kelly was murdered in the early hours of 19 June 2004 on Grafton Street, Dingle. As he got out of his car he was approached by two men who were armed with a gun. Liam attempted to run away but was shot as he tried to get into a nearby house. He died as a result of his injuries.
Anyone with information in relation to the death of Lucy Hargreaves is asked to call 0151 777 8617 or Crimestoppers anonymously on 0800 555 111.