Today marks a decade since the University of York chef vanished on March 18, 2009 at the age of 35.
Although no body has ever been found, North Yorkshire Police have been treating her disappearance as a suspected murder investigation.
Nine people have been arrested or interviewed under caution in connection with the investigation and police submitted files to the Crown Prosecution Service (CPS) in relation to a number of individuals, but there was insufficient evidence to bring charges.
On the tenth anniversary of when she was last seen, North Yorkshire Police said they are still waiting for information from the public to help them make major progress.
Detective Superintendent Dai Malyn said: "It remains the case that we strongly suspect key and vital information is being withheld that could provide the breakthrough that we all want to see, not least Claudia's heartbroken family.
"Unless we get information or intelligence to suggest that Claudia came to harm as a result of an opportunity taken by someone unconnected to her, me and the team still strongly believe the answer lies locally.
"As with some recent cold case successes, the breakthrough has come from the public and we still have confidence that this will be the case."
Following Miss Lawrence's disappearance, searches were initially focused on the route between her home on Heworth Road and the University of York.
Hundreds of officers across various forces were initially involved but the investigation has been scaled back over the years.
Mr Malyn added that the investigation has so far been hindered by a lack of CCTV around Miss Lawrence's home, as well as the fact that she had neither a smart phone or a social media profile when she vanished.
"We know also that her mobile phone didn't leave the area before it left the phone network," he added
"This again is a reason I don't believe she fell victim to an attack by a stranger.
"Also, we have no actual scene where something untoward may have happened to her despite fresh forensic assessments of her house, car and other locations."
The force explained how members of the public are still coming forward with information.
Despite being "well intentioned", much of this is based on speculation or theory, Det Supt Malyn said.
"The call we really want is the one that helps piece together the parts of the jigsaw we already know regarding her last movements and people she associated with and places frequented," he added.
Last week, Miss Lawrence's dad Peter told how he had to admit that he may never see her again.
He told the Yorkshire Post: "It is hard to say that, and I have never told anyone that before. But I have to come to terms with it as it may very well be the truth.”
Throughout the police investigation Mr Lawrence has been unwavering in his desire to keep his daughter's disappearance in the public eye.
He has conducted hundreds of interviews to stress the point that someone holds a key piece of evidence which would provide clarity over exactly what has happened to her.