The flight landed on Friday - July 4, the country's Independence Day - and Mr Mayer said staff announced the airline was struggling to get a hold of a coroner because of the occasion.
"I'm guessing he was enjoying himself somewhere on the national day."
When the plane landed, passengers were asked to stay seated to allow medical staff, police and fire crews to board.
The woman who had died was seated near the rear of the aircraft, he said.
Sergeant Karla Ortiz from Los Angeles International Airport police said CPR was performed on the passenger.
The coroner had now taken over the case because there no suspicious circumstances surrounding the death, Ms Ortiz said.
Mr Meyer said there was another delay of about an hour while a new aircraft was prepared for the remainder of the flight to the UK.
On top of that incident, when the flight landed at Heathrow, passengers were again asked to stay seated because of another medical emergency, he said.
"There wasn't much info given, but I'm guessing it wasn't serious because there wasn't as big a kerfuffle on that situation.
"When the steward announced that we had another medical emergency a few of us just couldn't believe our [bad] luck."
He got the impression from crew that the person was just unwell.
Civil Aviation Authority spokesman Mike Richards said Air New Zealand would need to contact the CAA about the woman's death.
"Incidents and accidents, and that's an incident, need to be reported to us within 14 days, so I'm imagining Air New Zealand - as a normal course of business - will report that to us."
It did not sound as if there was a problem with the aircraft that would concern the CAA, Mr Richards said.
Some took to twitter to discuss the events on board the flight.
One passenger Allister Homes tweeted that the flight, originally bound for Heathrow in London, had been delayed in Los Angeles.
"Our flight from LAX was delayed because sadly a passenger died on board the aircraft on the way to LAX."
He tweeted there was another problem at London, with passengers unable to disembark because of another "medical incident" on board the same flight.