Radio NZ reported that family lawyer Michael Kidd would be applying for bail today and he was about to file with the UN Human Rights Committee.
"Their right to life is going to be significantly impacted by going back to such a hostile environment," he told Radio NZ.
"There's a lack of fresh water, there's rising sea levels, a lack of ability to grow crops, danger from storms that are coming through, and frequent flooding."
He said the family faced a "serious life-threatening problem", especially the children, although the New Zealand courts hadn't agreed.
Mr Kidd said he was "hopeful" the family could stay in New Zealand and pointed out that while the country was taking refugees from Syria, we weren't so welcoming to Pacific refugees.