It is proposed that any such referendum would follow extensive consultation with Indigenous peoples to decide the form of words to be used in any amendments made to the Constitution.
The LCA also urged the parties to commit to ensuring Australia's laws and policies comply with the UN Declaration on the Rights of Indigenous Peoples and Australia's obligations under the UN Convention on the Elimination of All Forms of Racial Discrimination.
"Australia's support for the UN Declaration must be underpinned by real action to ensure our laws don't impinge on the rights of Indigenous Australians," said LCA president, Glenn Ferguson.
"All parties should commit to developing a framework for treaties and other lasting settlements with Indigenous communities."
Ferguson added that Australia is lagging well behind the rest of the world in this regard, as New Zealand, Canada and the United States have all concluded treaties with their Indigenous peoples.
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