Peter Lawrence spoke on the 11th anniversary of his daughter's disappearance on Wednesday, saying how it would take relationships to break or changes in heart for someone to come forward and shed light on the investigation.
North Yorkshire Police meanwhile said they would "never give up on Claudia until it is known who is responsible for her disappearance and suspected murder".
Miss Lawrence was last seen walking home from her job as a chef at the University's of York's Goodricke College on March 18, 2009.
The 35-year-old failed to show for her shift at 6am the following day, and was later reported missing on March 20 by her father.
What unravelled was one of the largest missing persons investigations ever carried out by North Yorkshire Police. Nine arrests were made, and in 2015 a file was sent to the Crown Prosecution Service, but despite this no person has ever been charged in connection with her disappearance.
Speaking from his home in York, Mr Lawrence said that despite the 11 years which have lapsed, he remains hopeful of answers.
The retired solicitor, now aged 73, has always said the answers to what happened to Miss Lawrence lie in the community.
"I think for someone sitting on information, it would take possibly a change in that person's relationship, or perhaps a fall out with a friend, for someone close to them to then come forward.
"It's difficult to grasp that someone in the community has been sitting on those answers. You wonder why they would have loyalties to someone else that would trump their conscience and what our family has been through."
Mr Lawrence featured in a programme on ITV on Tuesday afternoon, which revisited the Claudia Lawrence case.
Judge John Rinder's Crime Stories recounted the police investigation into the disappearance, speaking to family and friends of Miss Lawrence.
"It is very important for things to keeping appearing about Claudia in the media," Mr Lawrence added.
"Usually, after something has been in the media about her, the police do have people contacting them. It has been a few months since I last spoke to the police but perhaps after yesterday's programme, more people may get in touch.
"After they (police) conducted the last review about two or three years ago, there's not much else they can do unless someone gets in touch with a lead.
"I'm not terribly concerned about arrests and charges, but I am concerned about answers into what happened to my daughter."
Mr Lawrence remains an active campaigner and ambassador for the Missing People charity.
He has also used his experience to bring into effect the Guardianship (Missing Persons) Bill, which gives families of missing people the legal right to deal with their financial affairs if the person has been reported missing for 90 days.
Dubbed 'Claudia's Law', the law received Royal Assent in April 2017 and the following year Mr Lawrence received an OBE after being named in the Queen's birthday honours list for his role in founding the Bill.
In an interview with The Yorkshire Post last year to mark the 10-year anniversary of her disappearance, he admitted he "may never see her again".
In spite of this, Mr Lawrence has never given up hope.
A short statement released by North Yorkshire Police on Wednesday said: "It was 11 years ago today that Claudia Lawrence was last seen alive. Our thoughts remain with Claudia's loved ones on this poignant day.
"North Yorkshire Police will never give up on Claudia until it is known who is responsible for her disappearance and suspected murder."