During their first face-to-face meeting since Anthony Albanese won, the prime ministers are expected to sign a new green economy agreement to streamline financing and technology development.
Mr Lee is considered a senior ASEAN leader and has consistently argued for the West and China to find common ground rather than escalate tensions.
In Singapore last year, Mr Lee told the former prime minister Scott Morrison that Australia should focus on areas of mutual interest with China rather than ideological differences.
After their meeting, the Singaporean PM said that they didn't have to become like them and that they can't hope to make them like you.
The ABC understands that Mr Lee's visit will include a visit to the Australian War Memorial, as well as a meeting with New South Wales Premier Dominic Perrottet.
Mr Albanese is currently hosting his Papua New Guinean counterpart James Marape, and both men watched the Australian Prime Minister's XIII men's and women's teams defeat visiting PNG teams at Brisbane's Lang Park on Sunday night.
On Monday, both men will board an RAAF jet to Japan for the funeral of former Japanese prime minister Shinzo Abe, along with former Australian prime ministers John Howard, Tony Abbott and Malcolm Turnbull.
The international engagements come a month before Mr Albanese is scheduled to jet overseas for three consecutive foreign gatherings - the East Asia Summit in Cambodia, the G 20 leaders' meeting in Bali and the APEC in Thailand.
The ABC revealed earlier this month that French President Emmanuel Macron was planning to make his second visit to Australia, sometime after he and Mr Albanese attended the G 20 in Bali.