During the interview with Detective Inspector Stephen Kelly, Lundy took numerous deep breaths.
Mr Kelly told Lundy the investigation had mostly been completed.
The jury also saw a videoed interview of Lundy, again by Mr Kelly, which was taken two weeks after the murders.
He said his only theory about why his family was killed was because of a "burglary gone wrong".
He also spoke of a loving marriage and denied he and his wife were on the verge of separation.
Lundy told Mr Kelly he was under the impression his wife's new life insurance policy had been increased a payout to $500,000.
Earlier in the trial the court was told the policy had not come into effect by the time of the deaths and the amount was $205,000.
Mr Kelly told the court Lundy had contacted him in February 2001 and, unprompted, spoke about petrol thefts from outside motels.
The jury trial in front of Justice Simon France continues.