The news came during an emotional 24 hours for the All Blacks.
Mils Muliaina was also tearful yesterday as a fractured shoulder ended his All Black career, and Colin Slade was ruled out of the World Cup with a groin injury. They have been replaced by Hosea Gear and Stephen Donald.
Mr Lui, 78, had been in and out of hospital in Wellington for some time, and then developed pneumonia.
He was stable until Thursday night, but died on Friday morning. Bill and his wife Kura then faced the agonising decision of whether to tell their son before Sunday's crunch clash.
They decided to wait, so he would stay focused on the field.
"I thought it could affect his build-up to the test," said Bill. "I thought he should concentrate on the game and because I thought he'd want to come home - he's very family oriented."
After hearing how upset his son was, Bill called one of Weepu's team-mates to check on him.
He called his son again yesterday morning and he was doing okay.
It is Weepu's second bereavement blow in less than a year - his maternal grandfather, John Turner, died at Easter.
Weepu's brother Billy said the All Blacks squad had rallied around the halfback.
"He had to deal with it by himself but he had the team to support him."
Weepu is to arrive in his hometown of Wainuiomata this morning for the afternoon funeral service.
Bill Weepu said he and the rest of the family watched the All Blacks beat Argentina and were proud of Weepu's strong all-round game.
"Good to see him listen to what I tell him," he said. "I tell him to run with the ball more."
Weepu, who will join the Blues for next year's Super Rugby competition, has played 54 tests.
He overcame disappointment over his omission from the 2007 World Cup, and a broken leg suffered when playing for Wellington last year, to become a key member of the All Blacks' backline.