As well as private donations, the ACT government has contributed $10,000 in Olivia's name.

The kitchen bench and dining room table in the Lambert family's Ngunnawal home are overflowing with flowers and her parents, Kirsty and James, have been overwhelmed by the outpouring of grief and support from the community.

''I didn't expect this kind of response, it's really nice to know that Olivia evoked that kind of emotion and really reached out and touched so many people,'' Mrs Lambert said.

Olivia captured Canberrans' hearts with her determination and courage during a six-year battle with neuroblastoma.

The little girl was diagnosed with stage four of the deadly disease in 2006 and her fifth birthday was a milestone doctors said she would never reach. The bubbly girl who wanted to be a ballerina celebrated her eighth birthday in January.

And when Australian doctors gave up on the little girl, Canberrans raised more than $300,000 for treatments in Germany and the United States.

Mrs Lambert said Olivia's courage and spirit remained in her final days at Clare Holland House.

''If she thought she was inconveniencing us she'd say 'I'm sorry'- we'd say to her, 'That word is not in your dictionary', but she'd still say it,'' she said.

''I slept with her in the single bed and she'd wake up and ask, 'Mum are you comfortable?' She was worried about how we slept, she was always thinking about other people.''

Mrs Lambert said Olivia died peacefully at about 10pm on Tuesday.

''The last few days have been really hard - I still can't look in her room. I miss her so much I feel like I can't catch my breath sometimes.''

Chief minister Katy Gallagher wrote to the family after Olivia passed away.

Ms Gallagher told the family Olivia's courage had inspired the capital.

''I know there is nothing that I can say or do to ease the pain that you will be feeling with the loss of your beautiful daughter but I do hope that some comfort can be offered in the knowledge that Olivia's story touched everyone and that thousands and thousands of people will be thinking of you both and of Sarah throughout this most difficult time,'' Ms Gallagher said.

The Olivia Lambert Foundation, which was started to give Olivia and other children living with neuroblastoma a chance, will continue as part of her legacy but the couple said finding a cure for the disease and donations towards research were a more fitting tribute.

''There wasn't a cure for Olivia but maybe there will be one for other children … when I can I want to expand the scope of the foundation to help other children and families,'' Mrs Lambert said.

''What we really want to solve is the puzzle of neuroblastoma and the Sydney Children's Hospital Foundation for Neuroblastoma research and the Children's Cancer Institute of Australia's Neuroblastoma research both do good work.''

A memorial service for Olivia will be held at 11am on Tuesday at St John's Church, Reid.