Fairfax Media said that Lomu left Auckland Hospital in a stable condition on Sunday after a fortnight's treatment.
The 36-year-old was a star of the 1995 and 1999 Rugby World Cups and played 63 rugby union Tests for New Zealand between 1994 and 2002, scoring 37 tries.
Lomu had a kidney transplant eight years ago after illness ended his international rugby career.
Two weeks ago Lomu said he was seeking a second kidney and had lost 30 kilograms, down from 119 kilograms in his playing days
He now needs dialysis treatment for seven hours, three nights a week to keep him alive.
"We were hoping to see some improvement but nothing has made any difference, so the next step is to try to find a donor," Lomu said then. "I know I was fortunate to get the first transplant but there are more difficulties this time around."
"The thing about being human is that everybody has to die sometime. For me, the important thing is to ask 'Can you look in the mirror and say you've done everything to enjoy life?'."