The Crown alleges Lundy drove from the Foreshore Motor Lodge in Petone, Lower Hutt, to his home where he killed his wife and daughter in the early hours of August 30, before returning to Petone.
They alleged there were discrepancies in the amount of petrol in Lundy's vehicle when he returned to Palmerston North on August 30.
Sergeant Danny Johanson said that as part of the investigation into the deaths, he drove three return trips between Petone and Palmerston North in a similar car to Lundy's Ford Fairmont and recorded the kilometres.
The routes he took were slightly different each time and he recorded distances of between 146.16km to 150.2km.
On some of the trips, Mr Johanson also visited some businesses around Petone, but not all the places that Lundy also visited.
He said he went the most direct route to the businesses, but under cross examination by defence lawyer Julie-Anne Kincade, he said he did not know if Lundy followed that same direct route.
"[Lundy] must have driven further than you," Ms Kincade said.
He said while driving the routes to and from Petone he would accelerate quickly and brake heavily.
Ms Kincade calculated the fuel Mr Johanson would have used, with the route he drove, was 27 litres per 100km, which he accepted.
"The purpose of these trips were to establish some data," he said.
Mr Johanson also read a police report Lundy had given on September 16, regarding a missing jewellery box from the bedroom her shared with his wife.
Lundy gave police a detailed description of the box, inside and out, but apart from a few pieces of jewellery, he was unsure what other pieces his wife had kept in the box.
The court also heard from a mechanic who had serviced Lundy's car just over a week before the murders.
Cory Stevenson said aside from needing to replace the brake fluid and antifreeze, the car was in "perfect condition".
Former police officer Nigel Withell told the court he performed tests on Lundy's vehicle in March 2001.
He described attempting to siphon petrol out of the fuel tank and said he was unable to do it without breaking a flap based inside the entry to the fuel tank.
The flap was undamaged before his attempt.
Former Lower Hutt police officer Murray Rei told the court he was tasked to plot car thefts in Petone between July 1, 2000 and February 2001.
There were 58 cases of theft within that time, including two of possible petrol theft, he said.
Under cross examination by Ms Kincade he agreed that victims of theft did not always report thefts.
Meanwhile, telecommunications expert Peter McFarlane told the court that cell site information showed Lundy was in Petone when he used his cellphone at 12.37am on August 30 and was also in Petone at 8.54am, when he next used his phone.
