The 74-year-old was arrested last week and released on bail ahead of his first court date.
He appeared this morning before Judge Claire Ryan and sought name suppression until his next court date.
The court heard Lawes' wife did not know the full facts of the case and it could have a negative impact on her if his name was published.
Police "strongly opposed" the application and it was rejected by Judge Ryan who said the grounds for suppression - as outlined in legislation - had simply not been met.
A source told the Herald that Lawes' arrest came after an investigation into an international child pornography operation led by the FBI in the US.
He is alleged to have paid a significant amount of money to enable him to access live child sex shows.
It is understood the live sex shows were filmed in Asia and streamed here on a computer.
The investigation into Lawes was run by police here, and is ongoing.
As part of that investigation his computer and other devices and property were seized.
Further charges have not been ruled out.
Lawes did not enter a plea today.
He was remanded on bail until his next appearance in three weeks.
His bail conditions include surrendering his passport, not using any device capable of accessing the Internet and not having any contact with a person under 16.
