The controversial Canadian pair, who have stirred debate on free speech in New Zealand before they have even arrived, have been issued specific purpose work visas to visit New Zealand for 10 days for public speaking events.
Lees-Galloway said that although the Government, and he personally, found their views repugnant, there were no grounds under the Immigration Act exclude them.
"We have to follow the law, we have to follow what the Immigration Act says. The Immigration Act sets a high bar for excluding people and I think that's important," he told Newstalk ZB.
Lees-Galloway said reports that Southern and Molyneux had been banned from other countries were not correct, rather they were prevented from entering for specific purposes. A total ban would have meant New Zealand could have turned down their visa applications.
"That is a reason that may have been used under our Act. Being permanently banned from the UK or Australia would have triggered a response from us."
He had some advice for New Zealanders who didn't agree with their views.
"Don't go, don't attend ... . I think these people are mostly looking for attention and I think the best thing we can do is starve them of it."
Meanwhile, New Zealand Police said they would not charge for providing policing for public safety.
Southern has been hit with a $A68,000 ($NZ74,000) bill by Victorian police for protecting her Melbourne event tonight.
An NZ Police spokesperson said police made operational decisions which may result in extra resources being used to cover particular events for any number of factors.
"Each event is different and any operational decisions are made on a case-by-case basis. The role of Police is to ensure the safety of our communities. Police would not charge any member of the public for providing policing to public safety risks," the spokesperson said in a statement.
Southern arrived in Australia last week for a speaking tour in the main centres there. She told Sky News Australia's Andrew Bolt last night that the police were participants in protests against her because the bill for protection would encourage protests at other events and shut them down.
A group of politicians, lawyers and commentators, calling itself the Free Speech Coalition, has hired a lawyer to sue Auckland Council for banning the pair from using city-owned venues for their events.
It argues the council and/or Mayor Phil Goff breached freedom of expression under the Bill of Rights Act, and freedom from political discrimination under the Human Rights Act, by refusing to allow the speakers to use the Bruce Mason Centre.
