Stephen Nicholson showed no emotion as he was convicted at Winchester Crown Court of the murder of the 13-year-old as well as three counts of rape when she was aged 12.
The 25-year-old care worker of no fixed address, repeatedly stabbed Lucy in the neck and upper body in woodland at Southampton Sports Centre before leaving her to die in July 2018.
According to the detective in charge of bringing Nicholson to justice, the care worker preyed on vulnerable girls to satisfy his sexual appetite.
Nicholson was also found guilty of sexual activity with a child in relation to another girl in 2012, who was aged 14.
He was acquitted of a charge of sexual activity with a child on multiple occasions when Lucy was aged 13.
Detective Superintendent Paul Barton, of Hampshire Police, said Nicholson had exploited Lucy's family who had taken him in as a lodger when he had nowhere else to live and used their hospitality to target the 13-year-old for sex.
The court heard Nicholson - who had been best friends with Lucy's stepfather Richard Elmes since they were children - would keep pet reptiles in the house and he said he stored cannabis in a kitchen drawer to sell to friends and clients.
John Montague, senior prosecutor for the CPS in Wessex, said Nicholson killed Lucy to prevent her telling people they had a sexual relationship and claims she made that she was pregnant with his child.
He said: "The motive is that she was in a relationship with him and had been for a significant period of time and he had to shut her up in one way, and that's the only way he thought he could do that and he stabbed her round the throat."
The court heard how Lucy had kept a diary which detailed her sexual relationship with the defendant dating back to May 2017.
William Mousley QC, prosecuting said Lucy described "increasingly violent" sex which included descriptions of him grabbing her neck in her journal.
He also read a note titled "Abuse" which Mr Elmes found after it had gone through the washing machine which stated: "He would make me or rape me anyway."
Mr Mousley told the Court Nicholson had "an interest in underage sex" and exploited Lucy who he described as "vulnerable".
After the verdict, Mr Barton said: "I would describe him as cold and calculated, I would describe him as a paedophile and I think he is someone who only thinks about himself and has taken full advantage of this family that have looked after him, provided a roof over his head.
"He has targeted Lucy, taken advantage of her and when she wanted a relationship with him, he has taken the decision to silence her once and for all by brutally killing her."
Mr Mousley said Nicholson told police after he was arrested that on the night before her death, Lucy had sent him a Facebook message saying that she was pregnant.
The investigation into Lucy's death, described by the CPS as "one of the largest in criminal history" was hampered when Nicholson refused to give police his Facebook password.
During the trial, the prosecution had to rely on Nicholson's account of the contact he had with Lucy on Facebook after the contents of their messages were lost following a year of delays.
were only given a full log of communications between the pair on the day the trial started after the social media company delayed giving detectives access due to rules set by Facebook and US laws on providing access to accounts.
The delay by Facebook in unlocking Nicholson's account has prompted calls for reform from politicians and by Britain's most senior police officer.
After the verdict, Detective Inspector Lee Macarthur read a statement on behalf of Lucy's mother, Stacey White, outside court, saying: "I would like to thank from the bottom of my heart the support from our close family and friends during this harrowing time.
"The dedication from Hampshire Constabulary, the specialist teams across the country and the local communities helped to get justice for my precious daughter Lucy."