Senior officers announced a series of new lines of inquiry on the fifth anniversary of the day Miss Lawrence failed to turn up for work at York University in 2009.
North Yorkshire Police launched a review of the investigation last year after a new major crime unit was established by the force.
Yesterday, detectives were keen to deny reports that the new team had identified a prime suspect as they made a series of new appeals.
Detective Chief Superintendent Simon Mason, the force's head of crime, said: "I need to make it absolutely clear there is no prime suspect in this case."
Miss Lawrence was 35 when she was reported missing by her father, Peter, on March 20, 2009.
She was last seen at around 3.05pm on March 18, walking back towards her home, and that night she spoke to both her parents on the phone.
Her family believe something happened to her after she left for work early on March 19.
Detective Superintendent Dai Malyn, who is leading the new review of the case, said his team has spent two months re-examining Miss Lawrence's home in the Heworth area and this work supports that theory.