DETECTIVES said tonight they had received upto 40 calls after the case was featured on Crimewatch.
A number of callers also suggested names of people who may be able to help North Yorkshire Police solve the riddle of the 35-year-old's disappearance.
The detective leading the investigation tonight said the chef had been involved in relationships ''of complexity and mystery''.
Detective Superintendent Ray Galloway, told the BBC1 programme he was certain Miss Lawrence had not told her family or friends about some of her relationships.
The 35-year-old was last seen near her home in York on March 18 and did not arrive for a 6am shift at work the following morning.
The force has now formally classified the investigation into her disappearance as one of suspected murder.
Tonight, nearly 11 weeks since Miss Lawrence, originally from Malton, North Yorkshire, went missing, a television appeal showed reconstructions of her last known movements and interviews with her father, sister and closest friend.
The programme also featured previously unseen footage of the inside of the University of York chef's house on Heworth Road and home video footage of her as a child.
Speaking on the programme, Mr Galloway appealed for anyone who had been involved in a relationship with Miss Lawrence to come forward.
He said: ''As the investigation has developed, it's apparent that some of Claudia's relationships had an element of complexity and mystery to them.
''I am certain that some of those relationships were not known to her family or her friends.
''I need to know the details of those relationships, in fact I do know the details of some of them, and I would urge anybody that was involved in a relationship with Claudia, or knew of one that a friend, a colleague, a neighbour was involved in, please, if they're going to be discreet and if they want to actually enable us to deal with it in a controlled way, a confidential way, they need to pick up that phone tonight.''
Mr Galloway continued: ''I'm not here to judge Claudia's relationships, I'm here to investigate them. I need people to share that information with me.''
Miss Lawrence's friends and family have previously dismissed speculation that she may have had a secret boyfriend.
Comments: Our rules
We want our comments to be a lively and valuable part of our community - a place where readers can debate and engage with the most important local issues. The ability to comment on our stories is a privilege, not a right, however, and that privilege may be withdrawn if it is abused or misused.
Please report any comments that break our rules.
Read the rules hereComments are closed on this article