"I have walked my part of the road. Now I ask this country to walk the next part with us," he told a crowd of hundreds of people.
The Kerrupmara Gunditjmara man had just presented a kangaroo skin to Prime Minister Anthony Albanese, inscribed with a letter calling for national truth-telling.
"The time has come for us to look honestly at ourselves," the first line reads.
Mr Lovett brought the message on a slow, 38-day walk, covering more than 500km of winding rivers from Melbourne to the nation's capital.
The final part of the journey was completed alongside hundreds of people from Canberra's Reconciliation Place to Parliament House, where he was met by the prime minister on Wednesday.
The walk, completed with wife Renata and their children, ended 59 years to the day after a successful 1967 referendum that led to Aboriginal people being included in the national census.
But Mr Lovett said many of the wants of Indigenous Australians were still being ignored.
Establishing a national truth-telling process was one of three requests made in the Uluru Statement from the Heart in 2017, which the Albanese government later committed to implementing.
The Indigenous voice to parliament, which failed at a referendum in 2023, was just one part.
Closing the Gap reports show no progress and critical issues facing some Indigenous communities have become drastically worse, architects of the Uluru statement say.
"Would a national truth-telling process hurt anybody? Of course, not," Mr Travis said, suggesting the process was often misunderstood.
"No people can be free inside a story that is not true.
"Let's be very clear; everything that has been achieved for the betterment of our people has been done by us, for us."
Mr Albanese said there was still a long way to go for reconciliation with Indigenous people.
"There are bumps in the road," he said.
"It's not a straight journey, as progress never is. But I assure you that we'll continue to walk with you.
"We'll be a stronger nation when there is proper and full recognition of First Nations people, and of course a full acknowledgement of our history, the pluses and the negatives."
Uluru Dialogue co-chairs Pat Anderson and Megan Davis marked the start of National Reconciliation Week with a continuation of their call for constitutional recognition of Indigenous people.
The dialogue is the group of First Nations leaders who led work on the Uluru statement, issued as "an olive branch to the Australian people to move forward as a nation".
Governments continued to announce policies, reviews, inquiries and programs without proper consultation with Indigenous communities, the co-chairs said, showing the need for a voice had not diminished.
"What has become increasingly clear since the referendum is that the problems and issues facing communities have not disappeared but are further entrenched and, in some respects, have become drastically worse," they said in a statement.
Aunty Munya Andrews, of Evolve Communities, a group providing cultural awareness and reconciliation training, warned Australia was entering "a dangerous new phase of division".
"The recent public backlash against Welcome to Country ceremonies should concern all Australians," she said, noting booing of the procedures at recent Anzac Day services.
Aunty Munya added she was concerned by a growing narrative the ceremonies were divisive, when they were an act of reconciliation inviting people to come together through a shared love of Country.
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