His daughter, Karina Lester, said people travelled from across the country for the funeral, including South Australian Premier, Jay Weatherill, state opposition leader, Steven Marshall, South Australian Minister for Indigenous Affairs, Kyam Maher, as well as other state and federal politicians.
"Today really is a sad day but a day to celebrate this wonderful man," Karina Lester told ABC radio on Tuesday.
During his speech at the funeral, Mr Weatherill said: "We’ll miss his storytelling, his generosity of spirit, his kindness, his warmth".
"We’ll never forget his resolve, his love, and the achievements that arose from a life filled with purpose and faith.
"May his legacy always inform, inspire and enlighten us – to make us strive for a better, fairer world," he said.
"On behalf of the entire State Government, I extend my sympathies to the family and friends of Yami Lester – this man of immense standing and dignity," the Premier added.
State Liberal Leader, Steven Marshall, told NITV News: "It was a very powerful farewell service at Walatina on the APY lands. The service captured the life of a man who had made such a valuable contribution to the Anangu. Paul Kelly joined the service to perform Maralinga - one of Mr Lester's favourites."
Mr Lester was best known for his work fighting for the clean-up of Maralinga, the site of British nuclear testing in the 1950s, which eventually helped establish a royal commission in 1985 and subsequent compensation for those impacted.
The activist - who died late last month at the age of 75 - was left blind as a young man by the atomic testing which he called the "black mist".
He was awarded an Order of Australia medal for his services to Indigenous affairs and worked on land rights issues across South Australia and the Northern Territory.
"Lester, the man who put the “Y” in APY, who spoke up for his people, his language, and his law."
A moving tribute published at the APY Council website titled, From Stockman to Statesman: Honouring the Life and Legacy of Kunmanara Lester says:
"As family gather at sorry camp fires, we pause to remember a great Yankunytjatjara man. Anangu Pitjantjatjara Yankunytjatjara honours Kunmanara [word used in Yankunytjatjara for a deceased person] Lester, the man who put the “Y” in APY, who spoke up for his people, his language, and his law.
"Kunmanara took his own natural gifts—honed in stock camps, in the saddle, and on the road—and turned them to a new purpose in his life as an Anangu statesman. With his boundless energy, taste for adventure, and a wicked sense of humour, Kunmanara had a unique capacity to tell a yarn—In person and across vast distances over HF radio—to inspire Anangu and piranpa tjuta (non–Indigenous people) alike, to show them that truly anything is possible with the grit and determination of the stockman or stockwoman.
Mr Lester's funeral took place at the Walatina station on the APY Lands.