Martin Dales spoke out after North Yorkshire Police began searching ponds and woodland areas in Hutton Gravel Pits near York last week, more than 12 years after she was last seen.
In March 2009, the 35-year-old chef was reported missing by her father Peter Lawrence after she failed to turn up for work at the University of York, and detectives believe she was murdered, even though no body has been found.
Mr Dales, who was a spokesman for Mr Lawrence before he died at the age of 74 in February, said: “It’s callous beyond belief that people can hold onto misguided positions in relation to this matter.
“Out there somewhere are cowardly people, or a person, who know what happened and they’ve got to recognise what this is doing to Claudia’s friends and family.
“There are people who aren’t coming forward with information after all this time - it’s ridiculous.
“I think they’ve got to search their hearts, minds and everything else again and think of the people who have had to sit through all this, waiting to find out what has happened and where Claudia is.”
He added: “The key thing is to be supportive of the police. The fact is, this is a thankless task: going through the lakes and woodlands.
“It reminds me intensely of the early days, when they were searching the lakes on the University of York campus.”
Detective Superintendent Wayne Fox, senior investigating officer in the case, believes that several people know, or have suspicions about, what happened to Ms Lawrence.
Underwater search teams and forensic experts have been combing Hutton Gravel Pits for clues, but North Yorkshire Police has not revealed what prompted the search.
Speaking last week, Ms Lawrence’s mother Joan said the new search had left her in “utter shock” and she was “very, very churned up” about the latest developments in the investigation.
Ms Lawrence was last seen at around 3pm on Wednesday, March 18 in 2009, when she was walking to her home on Heworth Road and she spoke to her parents on the phone later that evening. Both said she appeared to be in good spirits.
The following day she failed to turn up for her 6am shift at the University of York’s Goodricke College and her father phoned the police the following day.
She was due to walk around three miles to work that morning, but never arrived, and her mobile phone – a silver Samsung D900 – and a blue and grey Karrimor rucksack have never been found.
Detectives said she appeared to have left for work that morning, as the bed had been made and there were breakfast dishes in the sink.
North Yorkshire Police said detectives have conducted two “extensive and exhaustive” investigations, taken thousands of statements, searched several scenes, trawled through thousands of hours of CCTV footage and even consulted experts from the FBI.
The force has also arrested nine people, but no one has ever been charged.