But despite a grim prognosis, Lilly continues to make strides with both her speech and motor skills, and will be starting kindergarten this year.
To help raise awareness of her condition, and eventually fundraise for new therapies, parents Amy and Grant have started a Facebook page, called Love for Lilly, detailing their journey.
"Life isn't always easy, but we wanted to show people miracles can happen," Amy said.
"Lilly's a fighter -- she's a full-on, happy, cheeky little girl."
Lilly, who is Amy and Grant's second child, was born on December 9, 2012, at the Mater Mother's Hospital in Brisbane, weighing a minute 915 grams.
Three days later, doctors discovered a severe brain hemorrhage -- common in premature babies due to their underdeveloped blood vessels.
"They said it was the worst [case] they'd ever seen," Amy said.
"They were telling us to prepare for her to go, and pushing us to switch off her machines. No parent wants to make that choice."
But as they were saying their goodbyes, Lilly opened one eye and squeezed her parents' fingers with her tiny hands.
"We knew she'd make it -- we said we were going to carry on with treatment."
Lilly was placed on a ventilator for six weeks and she was fitted with a Rickman's reservoir, a small pouch under the skin to collect and absorb the fluid from her brain.
She was later fitted with a shunt to help drain the fluid and, after 108 days in hospital and three brain surgeries, Amy and Grant were finally able to take Lilly home.
Eventually, the family returned to New Zealand, as they were ineligible for funding for the specialised equipment Lilly would need in Australia.
Lilly is currently unable to walk, uses a custom-made chair to sit upright for long periods, and has impaired vision and respiratory problems resulting from her early birth.
She recently had springs inserted in her skull to help expand her narrowly-shaped head, allowing for her brain to grow and develop.
Since then, she has grown "stronger and stronger", and is able to sit up and engage more with her surroundings and now has a few words of speech, including "mum", "brother" and "Grant".
"She's got a lot of energy -- she scoots around everywhere on her bum," Amy said.
"She isn't on any medications, and she can oral feed just fine.
"We were told she'd wouldn't be able to do anything; that she'd have to be tube fed and wouldn't be able to breathe on her own -- but she showed them."
Amy and Grant eventually hope to travel to the US to pursue NeuroSuit Therapy for Lilly, which would allow her to walk unaided with the help of a specially-made compression suit.
But, for the short term, they hope to see her walking with a frame, and to give her "the most normal life possible".
"We try to focus on the positives and not treat her any different," Amy said. "We take things day by day."
