The family had come to New Zealand to help Ms Lee settle into her new home before they returned to Hong Kong. She was driving at the time of the crash.
Yesterday, Ms Lee's former university described her as "a young woman of tremendous vibrancy and compassion", and on social media her friends mourned her loss.
Lucy Tang wrote on Facebook: "The impact you have made on the past 10 years of my life cannot be described with words.
"Thank you for all the rainbows and sparkles, it's not easy saying goodbye to a best friend."
Ms Lee was a computer science major in the College of Liberal Arts at Tufts University, Massachusetts.
A message from university president Anthony P Monaco, posted on the Tufts website, said she was about to begin a study-abroad programme at the University of Auckland through Arcadia University.
"This loss is a tragedy for all who knew and loved Julia and her parents, and for Julia's faculty members, advisers, classmates, and friends," he said.
"This is also a loss for all members of the Tufts community. Julia was a young woman of tremendous vibrancy and compassion, and she will be deeply missed."
Two services were scheduled to be held at the university's Goddard Chapel, and information was provided to students and staff about how to access counselling and support services. On Twitter, Roy Yang said: "Experienced death of a friend for the first time ... puts perspective in a lot of things. R.I.P Julia Lee. I know you're in a better place."
Another Twitter user, Jose C Hernandez, posted: "I feel so sad for the death of Julia Lee and her relatives. My sincere condolences to the #Tufts community and her friends."
A University of Auckland spokeswoman expressed the institution's "profound sympathy" to the family and friends of the Lee family.
The crash happened about 3.45pm on Tuesday, when the car Ms Lee was driving crossed the centre line and collided head-on with a logging truck.
Her brother, whose name the Herald had not confirmed last night, was in the front passenger seat, while the siblings' parents were in the back.
It is understood Mr and Mrs Lee were not wearing seatbelts.
Investigations are continuing.
- additional reporting: Sophie Ryan