Sheetal's brother-in-law Hinesh Kumar and a female relative identified the bodies at the scene. The family is devastated with grief and are being consoled by friends and family.
A hearse arrived at the lake earlier and family members have asked for time to grieve.
Emotion is high, with tears and family members hugging and supporting each other at the lakeside.
A large group of friends and family of the couple, who have a 5-month-old daughter, were at the lake this morning.
The child was being cared for by family members of the Fijian Indian couple, originally from Suva.
Superintendent Lane Todd earlier confirmed that two bodies had been found in the lake. He confirmed that the male was 27 and the female 31.
"This obviously a very tragic event for the wider family, many of whom are here at the moment," he said.
"What appears to have occurred is that about 5.40pm last night the vehicle has driven into the lake and we're determining exactly what the causes are."
He said there has been "speculation" about what has happened but it's too early to confirm anything.
Police have arranged for a crane to pull the car, which was found on its roof, out of the lake early this afternoon.
It was found at a depth of around 6m, Todd said, with poor visibility.
He wouldn't confirm exactly where the bodies were found, whether they were inside or outside of the vehicle.
Victim Support and police liaison officers are with the family.
"We are totally lost. We don't know what to do now, we don't know what the next step will be."
The close-knit Fijian Indian community in Christchurch is a big help, the family say.
They described the couple as "very friendly, very happy people".
"They were really fun to be around, really nice," Kumar said.
Sheetal came to New Zealand last year, but her husband has been in New Zealand for about five years. He ran an air-conditioning company and was well known in the community. He was teaching his wife how to drive so she could find work.
The police national dive squad were due at the scene earlier this morning but were delayed, not arriving until 10am. They went into the lake about 10.30am.
The family is critical of the time it's taken to get to the couple.
"I just want to see them. That is all," Kumar said.
"If this was Fiji, we would've have got in and got them out ourselves. We would not wait around."
Earlier attempts to find the couple were unsuccessful when a diver indicated the water was too deep to reach the car.
Police staff and other emergency services stayed near the lake overnight, trying 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.
Firefighters and police tried 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.
It is just 200m from Checketts Ave where Helen Milner, dubbed the Black Widow, murdered her husband Phil Nisbet in 2009.
Checketts Ave is also where builder Michael McGrath lived before his mysterious disappearance in May.
Police searched the lake during their massive, and so far unsuccessful, hunt.
"With the Black Widow and Michael McGrath and now this, it's pretty weird and sad for the families," said local resident 16-year-old Angus Lowe.