A woman learning to drive accelerated into the lake last night, and her husband tried to rescue her.
A hearse arrived at the lake earlier and family members have asked for time to grieve.
Avneel Ram (26) had dived in to try and reach his wife, Sheetal (31), when their car slipped into the water.
"He is a hero to us. He tried to save his wife. Not everyone would do that," Sheetal's brother-in-law Hinesh Kumar said.
Mr Ram was teaching his wife how to drive and it appeared she accidentally accelerated into the lake, Fairfax reported.
The couple's 5-month-old child is being cared for by family members of the Fijian Indian couple, originally from Suva.
The close-knit Fijian Indian community in Christchurch is a big help, the family say.
"They were really fun to be around, really nice," the family member said.
Mrs Ram came to New Zealand last year, her husband has been in New Zealand for about five years. He ran an air-conditioning company and was well-known in the community.
The police national dive squad was due at the scene earlier this morning but have been delayed.
"If this was Fiji, we would've have got in and got them out ourselves. We would not wait around."
The Police National Dive Team was due to arrive this morning to look for the pair who remain unaccounted for after the car disappeared into the former quarry lake.
Earlier attempts to locate the couple were unsuccessful with a diver indicating it was too deep to reach the car.
Police staff and other emergency services remained in the area and in the lake last night, working to establish what happened and speaking to people who saw the tragedy unfold.
Witness Jordan Fleming said he was walking his dog past the Westlake Reserve when he saw a woman in a red hatchback in the car park, and a man outside trying to open the driver's door.
"I heard the accelerator go and that's when the car went off the bank down the hill into the lake," he said.
The man jumped in and swam after the sinking car, diving and resurfacing several times, Fleming said. Then he dived and did not reappear.
Police were called at 5.45pm to reports that a vehicle was submerged in the lake.
Both firefighters and police attempted to dive down to the vehicle to see if anyone was trapped inside.
Other witnesses said two other people who tried to save the pair were taken away by ambulance.
A diver went into the lake but came up indicating he could not reach the vehicle, locals say.
The lake sits in the middle of a housing development in Halswell. Residents say it's a deep former shingle quarry popular with runners, walkers, cyclists and children feeding ducks.