What has to happen for the bans on nuclear energy to be lifted? Is a referendum required?

It is first important to understand there are multiple bans on place under different jurisdictions. Under no circumstances would a referendum be required to lift the ban on nuclear energy given that the bans on nuclear energy are not in the constitution. However, there could be a plebiscite if that was desired. According to the Parliamentary Education Office:

"A plebiscite is a national vote on a question that does not change the Australian Constitution. Governments can hold plebiscites to test whether people support or oppose a proposed action on an issue. The government is not bound to act on the result of a plebiscite."

To lift the bans across the federal, state and territories is for those parliaments to lift the ban. For example, for nuclear power to be allowed at a Federal level, 76 members or more in the House of Representatives also known as the lower house, must pass a bill repealing the ones that implement a ban. From there, it goes into the Senate, also known as the upper houses where 39 members or more must pass the bill. Once that occurs, the bill is then sent off to the Governor General to be signed into law. Once the bill takes effect, nuclear power will be legal.