Derek Rogers, 55, of Catford, south-east London, told the court that Lynne, 17, had been offered a job stewarding executive flights with a salary of pounds 14,000 by a man who had rung her four times.
She arranged to meet the man at Charing Cross railway station in central London, on 4 September 1991. They were then going to drive to Shoreham in Kent to take a helicopter to Gatwick airport.
'I was very concerned about it. But she told me not to worry, that I worried too much,' Mr Rogers said.
Scott Singleton, 36, of Broadfield, Crawley, West Sussex, denies murdering her between 4 September and 7 September.
Five days after the job interview, Lynne's body was discovered hidden in brambles off a country lane in Rotherfield, East Sussex. She had not been sexually assaulted.
Mr Rogers broke down as he read a note he had written for his daughter on the morning of the interview. He reminded her to wash behind her ears and to ring him regularly.
Spencer Clark, 25, Lynne's boyfriend, of Beckenham, south London, said he had also thought the job sounded suspicious.
'She listened to me, but I think the offer of the money clouded her rational thinking,' he said.
Mr Clark had told Lynne to ring Africa Hinterland, one of the travel agents she had sent her curriculum vitae to because the man said the company had given him her CV. 'But she never did,' Mr Clark said.
After Lynne left for the job interview, Mr Rogers tried to ring Africa Hinterland, but the number was unobtainable.
Mr Clark also suggested that Lynne borrowed a mobile telephone to take to the interview. 'But she never did. I also requested that she rang for me at 12 o'clock,' he said.
By 10.30pm Mr Rogers had not heard from his daughter and he rang Mr Clark. Together they went to Catford police station to report her missing.
Her sister Suzanne, 20, told the court that she had spoken to the man twice and he had refused to leave a name or telephone number.
'His voice was very distinctive. It was very businesslike and abrupt. He just wanted to speak to Lynne,' she said.
She said Lynne had sent copies of her CV to companies in the hope of finding a job after being made redundant by a firm of investment brokers. On the telephone, the man had claimed he was anxious to talk to Lynne after receiving her CV.
The man, who gave no name or company details, said he worked with businessmen travelling for the day to the Netherlands, Belgium and France. Lynne would be based at Gatwick as a secretary mainly, occasionally going on flights to steward passengers.
The prosecution claims the man was Mr Singleton.
When Suzanne Rogers told Lynne about the call, she was 'surprised' because she had not applied to Gatwick and had stated on her CV that she could not type properly.
Richard Ellis, a farmer from Rotherfield, told the court that he had seen Mr Singleton's car within a quarter of a mile of the place where Lynne's body was discovered. He wrote down the car number plate because it was 'parked oddly', he said, adding: 'It looked as if someone was trying to conceal themselves behind the door pillar.'
John Rumens, a gardener, told how he had discovered Lynne's body five days after she went missing.
The hearing continues today.