A lawyer for the couple told the Belfast High Court that his clients were being unlawfully denied equal rights with religious groups.
Opening the case in front of Mr Justice Adrian Colton, the couple's lawyer Steven McQuitty said all they wanted was the same protection afforded to those of different belief systems.
Mr McQuitty said as the law stood in Northern Ireland the couple's wedding on 22 June would be "legally meaningless".
He told the court the case was of "huge public interest", highlighting that there were 4,290 humanist weddings in Scotland in 2015, more than those conducted by the Church of Scotland.
"Religious people from Pagans to Free Presbyterians and everything in between enjoy a substantial legal privilege under law," he said.
"In a sense the State gives its legal blessing to such marriages."
He claimed the law "denies the same privilege to equally valid groups".
Humanism is a non-religious belief system that rejects the concepts of a higher deity or afterlife.
Humanists adhere to a scientific view of the world and believe humans steer their own destiny.
Ms Lacole, from Belfast, and Mr O'Kane, from Co Derry, are taking a case against the General Register Office for Northern Ireland and Stormont's Department of Finance.
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