The prosecution are trying to prove that Mr Lyttle lied about seeing Mr Hall's quad bike in a different location two days after the alleged murder.
The crown says Mr Hall was killed on 27 May 2011, shot in the head by Mr Lyttle.
At the time, a large search and rescue operation was conducted north of Whanganui because Mr Hall's quad bike was found at the top of a track leading into dense bush.
Mr Hall's son, Damien Hall, saw the quad bike in question at the top of the track on the Saturday, but only from a distance.
He said when he was at his dad's property during the search effort on 1 June, the quad bike had not moved from where he had seen it four days earlier.
"It was still in the exact same location as where we'd seen it on the Saturday," he said.
"In fact, the police even took me to that same vantage point to make sure it looked as it did on the Saturday."
But the defence said the bike did move, because Mr Lyttle saw Brett Hall on the Sunday at his camp, and he had the quad bike with him.
The Sergeant Major of the Army, Clive Douglas, was called in as an expert tracker when Mr Hall went missing.
He said it was nearly impossible that the quad could have been up the track more than once in a ten day period.
"What we came up with and hence why the 10 days, is that based on what we saw, it's virtually impossible for that quad bike to have gone up there more than once," he said.
"When you look at that position, that's a key indicator because, to go forward, that grass ahead, it would have left something, and during that time period we would have picked it up."
The quad bike was left atop a steep, grass track branching off from Mr Hall's property.
The track was described as being no more than three metres wide.
Mr Douglas explained to the jury his advanced techniques for tracking a person, animal or, in this case, vehicle, along different types of terrain.
He said a quad bike flattens grass as it rolls across the ground, and even disturbs the ground where worms would have surfaced.
Based on the way grass was pressed, and the fact a spider's web near the quad bike was not disturbed, he said it was highly unlikely the quad bike had returned to the camp during the time period in question.
A former police officer who was involved in the search, Alan Spooner, also said there were no signs of a return journey.
"... four wheeler that big and in such a narrow area, if that bike had turned around and come back down at any point there would have been quite distinct turning lines," he said.
"There's no way you could turn around in one circle. You'd have to do a 10-point turn, for lack of a better word, to come back down."
Defence lawyer Elizabeth Hall cast doubt over the findings of Mr Douglas, talking about the type of grass on the track and the length of time it took for a tracker to be called in.
It was not until the following Saturday, 4 June, that Mr Douglas looked over the tracks.
She asked if Mr Douglas had conducted any kind of experiment, seeing how the grass would rebound after bring driven over by a quad bike.