Miss Lawrence, then aged 35, was last seen alive on the afternoon of Wednesday, March 18, 2009, as she walked home from work at York University. She did not turn up for work the following morning, after which she was reported missing.
Speaking on the BBC's Crimewatch programme tonight, Detective Superintendent Dai Malyn said a CCTV review had revealed what could be "highly significant" footage of a vehicle seen near Miss Lawrence's house on March 19.
The old-style light coloured Ford Focus hatchback car was seen driving along Heworth Road at 5.42am. As it approached level with Miss Lawrence's house the car's brake lights came on.
Det Supt Malyn said: "The fact the car appears to brake may indicate you (the driver) saw something that could be very important to us."
Officers also want to trace the owner of a white Vauxhall Astra van seen on CCTV parked on the road opposite Miss Lawrence's house, towards the Costcutter shop and the fish and chip shop, on March 18. It was there for at least 30 minutes from 9.01pm.
A first public appeal has also been made to trace a man seen on Heworth Road at about 2.30pm on an unknown day during the week Miss Lawrence went missing.
The man is described as white, clean shaven, slim build, 5ft 9in to 5ft 10in tall, aged in his 30s, with dark hair stylishly cut with a fringe.
He was wearing a mid hip-length, light tan coloured 'Mac' type jacket, smart dark-coloured jeans or trousers and dark-coloured footwear. He was carrying a small dark rucksack over his shoulder.
The man was laughing on his mobile phone and appeared to be looking for a particular house. He approached a house and when the door opened a woman of similar description to Miss Lawrence emerged also on her phone.
The woman initially appeared shocked at seeing him, suggesting he was not expected, but eventually led him into the house.
Detectives also want to trace a man standing outside Miss Lawrence's house between 6.45am and 6.55am on March 19.
He is described as white, aged 55 to 65, about 6ft tall with a full head of medium-length grey hair.
He was wearing an unfastened matt sandy-coloured 'Mac' style jacket which came just below the knee.
Det Supt Malyn said: "This time would have been after she had left for work if she had walked. Therefore why this person would be so close to her door remains a very important fact we need to establish."
The CCTV footage, further information relating to the sightings and all new leads revealed as a result of the review can be viewed online at www.northyorkshire.police.uk/13147.
Anyone with any information that could assist the investigation, should contact North Yorkshire Police on 101, or Crimestoppers, which is offering a £10,000 reward, on 0800-555-111.