Love has poured out since Wallace's death, she said, with support coming from both New Zealand and Australia.
"The family are doing really well, they've been surrounded by an incredible amount of love from, it's quite a big family, and they've come together strongly," she said.
"That's been a real source of comfort but also it's the community and I guess the rugby league community in particular.
"Zae played rugby league in New Zealand and Australia, they've come over from Australia, they are really surrounding him with lots of love."
He captained Westlake Boys' High School and also played for national-level representative sides before penning a contract with the Gold Coast Titans under-20 side.
Wallace had recently returned to Auckland and started a new career as a scaffolder while playing rugby league for the Northcote Tigers.
He only played one game before falling ill and because he wasn't eligible for ACC at the time, a Givealittle page was created for his recovery.
However, the page, which has raised more than $32,000, said in an update the funds would help family with funeral expenses.
Lees said his family was grateful for all the messages they had received following the death of "an amazing young man".
"He was always involved in lots of things and lots of different people … physically he wasn't a big man but he was very big-hearted," she said.
"The family would like to extend their thanks for all the love and support they've received over this really difficult, long time."
Former clubs, unions and friends pay tribute
Former clubs, teammates, friends and family have all paid honour to the promising football player, including New Zealand Rugby League.
In a statement, it passed on its condolences to the Wallace family and their friends, calling him a "young talent that will be sorely missed".
"Wallace spent that season with the Titans then joined the Burleigh Bears in the Intrust Super Cup," the NZRL said in a statement.
"Playing at halfback and being the youngest member of the squad, Wallace was one of the Akarana Falcons star performers in their National Premiership championship victory in 2016.
"That same year he was named Auckland Rugby League's College Player of the Year.
"Wallace is described as a 'lovely and cheeky' young man, who had a great sense of humour and a great bunch of friends."
Rest in Peace Zae, a young talent that will be sorely missed. Our deepest condolences go out to Zae's whanau and friends.
Posted by New Zealand Kiwis on Saturday, June 1, 2019
Warriors halfback Chanel Harris-Tevita told Wallace to "rest easy brother" on Facebook.
Northcote & Birkenhead Tigers Rugby League said they were extending their "heartfelt sympathy" to Wallace's extended family.
They said on Facebook the death of the young man was devastating and would provide further details when they became available.
The Gold Coast Titans also paid tribute.
"It is with heavy hearts that we pass on the news of ex [Gold Coast Titans] U-20s player, Zae Wallace's passing this morning," they said yesterday.
"Zae's family and close friends have been humbled by your support and love, and blessed with the realisation he has touched so many lives in his too short a time with us."
Elsewhere, Counties Manukau Touch posted about Wallace's death.
"It is with heavy hearts that we share with you, Zae has lost his battle and passed away earlier today. He was just 20 years old," they wrote on Facebook yesterday.
"The young sportsman, who returned to Auckland this year following a stint with the Gold Coast Titans under-20 side, had been in an induced coma at Auckland Hospital.
"Zae was an amazing footy player, and well known throughout all codes in Auckland. Many of our Counties Touch Whanau were good friends with the young star."
Semi-professional rugby league club the Burleigh Bears, who Wallace played for formally, said his family are in their thoughts and prayers.
It is with great sadness that we inform you of the passing of Bear #340 Zae Wallace.
Zae was loved by all at the...
Posted by Burleigh Bears on Saturday, June 1, 2019
"It is with great sadness that we inform you of the passing of Bear #340 Zae Wallace," it said on Facebook.
"Zae was loved by all at the Burleigh Bears and while he will be missed won't be forgotten.
"The Club would like to offer its condolences to Zae's family and friends especially parents Rose and Wayne and siblings Kirsten, Vann and Leigh in these tough times."
Meanwhile, Westlake Boys' High School have taken to Twitter to pay tribute to their former student and rugby league captain.
"The Westlake community is deeply saddened with the loss of former student, Zae Wallace. Sending all our love to his family and friends," it posted.
