The 20-year-old aspiring model had just finished work as a typist at a radio station and was on her way to meet her fiance John Fitzgerald.
A coroner's 2016 report ruled Ms Butterworth was murdered by Geoffrey Charles Hunt, who strangled her in his car after she accepted a lift.
Her body has never been found despite extensive searches.
Mr Hunt, who denied any knowledge during the inquest of what happened to Ms Butterworth, has never been charged.
Tasmania's director of public prosecutions determined in 2017 there was not enough admissible evidence to charge Mr Hunt.
Almost 55 years since her disappearance, investigators have renewed calls for information they hope can deliver justice for Ms Butterworth and her family.
Detective Inspector Mark Burke said police had received new information this year, but no additional intelligence specific to Mr Hunt.
"Some witnesses have come forward with information that was put forward in the coronial (inquiry)," he said on Friday.
"We believe there are people in the community who know what's happened to Lucille ... and we'd like to hear from them."
Tasmania Police previously publicly apologised for their handling of the case after the coronial inquiry heard of multiple investigative failures.
Mr Hunt was jailed for 25 years in 1976 after pleading guilty to raping and murdering young Hobart car saleswoman Susan Knight.
Geoffrey Charles Hunt denied murdering Lucille Butterworth. (Rob Blakers/AAP PHOTOS)
Two officers who gave evidence at the inquest said Mr Hunt confessed to killing Ms Butterworth when they initially questioned him about Ms Knight.
They said Mr Hunt's confession was not formally recorded because they "still had quite a lot to do" in relation to charges relating to Ms Knight.
Mr Hunt's statement was not followed up because a detective inspector said it was the "wrong track", according to the coronial report.
Senior officers initially viewed Ms Butterworth as a runaway, rather than a "proper" missing person case.
Efforts were made in 2000 to continue the investigation but an interview with Mr Hunt conducted that year was inexplicably lost.
"I can't undo the ills of the past but I can apologise to the Butterworth family for the matter (and) how it was investigated," then-Commissioner Darren Hine said in 2016.
Ms Butterworth was last seen wearing orange work clothes and a dark coat.
She was killed on a stretch of the Lyell Highway, about halfway between Granton and New Norfolk, north of the bus stop in suburban Claremont, the coroner ruled.
Police have reminded people information can be reported anonymously.
"This is a tragic case that has caused a family massive pain and suffering," Det Insp Mark Burke said.
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