In Australia, Mr Lee Kuan Yew is widely remembered for a rebuke he famously delivered more than 30 years ago.
During a visit in 1980, Mr Lee warned that Australia needed to open its economy and try to reduce inflation and unemployment, or risk becoming the "poor white trash of Asia".
Today, Mr Lee's warning is widely regarded as typically stern, but both prescient and fair.
Delivering a condolence motion speech in the Australian Parliament on Tuesday, Prime Minister Tony Abbott noted Mr Lee's warning and praised him for "spur(ring) this country at a critical time in our history to be better than we might have been".
Praising Mr Lee for helping to achieve "one of the most remarkable economic success stories in history", Mr Abbott said the "great nation-builder" had been a trailblazer for other countries such as South Korea and China.
"Lee Kuan Yew did not just lead his country; he made his country," he added.
"Singapore and Australia are natural partners, and I hope that over time, our relationship with Singapore will be as easy, as close and as familial as it has long been with New Zealand. And, if so, that too will be part of Lee Kuan Yew's legacy."
The death of a man many called a "political giant" has this week generated a vast amount of coverage in Australia, where he was both praised for his transformation of Singapore and condemned for his harsh approach to the political opposition. But almost every article and news broadcast referred to that 1980 comment - and it is now largely seen in Australia as sage advice.
Indeed, the comment appears to have had a lasting influence, perhaps more than Mr Lee could have foreseen.
When he returned to Australia in the 1990s and was reminded by reporters of his remarks, Mr Lee would acknowledge that Australia had avoided its potentially bleak fate. His remark, he often added, was not meant to "diminish" Australians, but to spur them on.
Most observers believe that this was in large part because Australia had changed course and headed in the direction that Mr Lee had been advocating, towards a more open economy and a more open approach to the nation's place in the region. In the process, Australia and Singapore have become increasingly close trading and diplomatic partners.
This influence over Australia's development was noted this week by Mr Bob Hawke, who was prime minister from 1983 to 1991 and steered the country through a period of liberal economic reforms.
Saying Mr Lee's words were "right", Mr Hawke described his old friend and golfing buddy as an outspoken leader who had a "great influence on this country and on my own approach to my task here as prime minister".
"His harsh but fair comment helped galvanise my determination to undertake the reforms that would save us from that fate and set us on a better path," he wrote in The Australian Financial Review on Monday.
"I doubt that I ever enjoyed more intellectually stimulating conversations with a fellow leader... A great bloke and, by any standards, a great man."
Mr Hawke's successors continued to regard Mr Lee as a source of wisdom on the region and its leaders.
As Australia began to prosper, bilateral ties blossomed and Singapore became one of its biggest foreign investors. Singaporean students have long flocked to Australian universities, while Australia's major banks, mining companies and engineering firms all have offices in Singapore.
According to Australia's Department of Foreign Affairs and Trade, Singapore is now the country's largest trade and investment partner in Asean and its fifth-largest trading partner overall. Fittingly, in 2003, Australia signed a free trade agreement with Singapore - its first such open trading deal in 20 years.
Little surprise then that Mr Lee received warm praise this week from Australian leaders, including Prime Minister Abbott.
"Our region owes much to Lee Kuan Yew," Mr Abbott said.
"Here in Australia and beyond, leaders sought and learnt from his wise counsel… At every stage, Australia and Singapore have stood shoulder to shoulder. We continue to do so today, as we salute one of the significant leaders of our time."
Analysts said the roots of Mr Lee's early reservations about Australia could be traced back to the mutual distrust between Canberra and the ascending local leadership in pre-independence Singapore. Australian intelligence officials reportedly feared that Mr Lee would support the communists in the region and wanted Singapore to be part of Malaysia.
Dr Alison Broinowski, a researcher at the Australian National University College of Asia and the Pacific, said Mr Lee received "condescension from Australian leaders" during his early years as leader. As Singapore's economy boomed, Dr Broinowski said, Mr Lee "relished" the opportunity to point out to Australia that it was falling behind.
In Australia, most analysts this week gave high praise to Mr Lee's nation-building legacy but criticised his stifling of the political opposition and of press freedoms.
"Lee Kuan Yew built Singapore into a fully developed economy, but he left it a half-developed democracy," columnist Peter Hartcher wrote in the Sydney Morning Herald on Tuesday.
Said Dr Broinowski: "There have been some shudders at the way opposition leaders have been treated and at some of its social policies, but there has been no doubt about Singapore's success."