Last year the Justice Select Committee last year recommended to delay a decision because of concerns about rights to freedom of expression and religion.
Robertson said Lubeck's bill would be adopted as a Government bill if Labour was re-elected and suggested NZ First didn't support banning the practice during this last term.
"Obviously it's been a Labour Party policy... but what we haven't been able to do is get full Government support for that."
Robertson confirmed the Greens supported the bill.
The ban on conversion therapy forms part of Labour's Rainbow policy which was unveiled by their spokesman Tāmati Coffey at a cabaret bar on Cuba St in Wellington.
Coffey said conversion therapy was based "on the misguided idea that people are wrong or broken because of their sexual orientation or gender identity".
"This is fundamentally wrong," he said.
Coffey said the practice had been linked to severe adverse mental health issues, including depression, anxiety and suicidal ideation.
"It is a practice that causes harm and is out of place in the kind, inclusive and modern country we are," he said.
The ban would make it a criminal offence to advertise or offer to perform conversion therapy, perform conversion therapy and knowingly take someone out of New Zealand to receive conversion therapy.
Alleged offences would be investigated by the police and those found guilty would be punished with a fine or imprisonment, depending on severity.
Labour has also promised to:
• Invest $4 million in existing Rainbow youth mental health services
• Work with schools to provide gender neutral bathrooms
• Ensure healthcare was responsive to the needs of trans, intersex and gender diverse people
• Review adoption and surrogacy policies with a view to removing discriminatory practices
In 2016, the United Nations Committee on the Rights of the Child recommended New Zealand develop and implement a child rights-based health-care protocol for intersex children.
About one in 2000 children are born intersex - about the same ratio as children who are born with red hair.
Labour committed to doing this in its next term to prevent unnecessary medical interventions on intersex infants and ensure binary gender assignment wasn't automatically presumed to be the best-case outcome.
Coffey said there was still a lot of difficult process and outdated assumptions in adoption and surrogacy for Rainbow families.
"I know from my own experience where my partner and I had to formally adopt our own biological son that we need to modernise the law."
