He said that in order to arrange Lawson's visa "in a timely manner", Immigration New Zealand's London office granted her a "special direction" visa.
This visa was given to people who had been excluded or deported from another country, convicted and sentenced to five or more years in prison, or convicted and sentenced to 12 months or more in the past 10 years.
Immigration officials believed the waiver was required because of British media reports that said Lawson had been refused entry to the US after publicly admitting to cocaine and cannabis use. She admitted her drug use at a fraud trial last year, but did not have a conviction.
After reviewing Lawson's visa application and information provided by a London-based lawyer, officials found that she should not have been categorised as an excluded person and was eligible for a visa after all.
"We currently have no information to indicate that she was excluded from the United States," Mr Carley said in the letter.
Lawson's New Zealand-based lawyer Megan Richards said INZ's response "was satisfactory from our client's perspective... ultimately everything worked out in the end."
The fact that Lawson needed special permission to enter New Zealand attracted international media attention.
It also raised eyebrows in New Zealand because some convicted criminals had not required special direction to enter the country.
"Wolf of Wall Street" Jordan Belfort, who is speaking in Auckland later this month, was eligible for a visa because his fraud convictions were not serious enough to warrant a special direction visa.
In correspondence to media, Immigration New Zealand noted that US rapper Snoop Dogg required a waiver to perform in New Zealand in January because he had drug convictions.
Lawson travelled to New Zealand to do publicity work for chocolate maker Whittakers.