He noted the then teenager had aggression problems and was resistant to change.
But he had not seen Lanza for some time when the 20-year-old killed 20 pupils and six other people at the elementary school.
Authorities in the US have not raised concerns about his treatment of Lanza, but there were allegations of misconduct and "possible boundary violations" over an alleged relationship he had with a patient.
US media have reported a former patient's claims she and Dr Fox had sex in his office, went out for dinner and spent time on his boat.
The investigation report said his interactions with the woman, "exceeded the boundaries of a professional doctor-patient relationship".
Dr Fox signed an affidavit in 2012 voluntarily surrendering his licence to practise psychiatry in the US.
In doing so, he admitted "no guilt or wrongdoing", but agreed that if he applied to practise again, the allegations made against him would not be contested in front of the Connecticut medical authorities.
He said the purpose of the agreement was to "resolve" the matters against his licence, according to the affidavit witnessed by a justice of the peace in Hamilton.
By the time of the Sandy Hook massacre Dr Fox had given up his US licence and was living in New Zealand.
Dr Rees Tapsell, the Waikato DHB clinical director of mental health and addictions, confirmed that Dr Fox was employed as a psychiatrist.
"[He] is fully registered and fully credentialled to practise in New Zealand. He has vocational registration with the Medical Council of New Zealand [and] is a competent psychiatrist and a good addition to the mental health team at Waikato DHB."
But specific questions about what the hospital knew about his past could not be answered because staff with that information were unable to be contacted, a spokeswoman said.
Dr Fox is allowed to practise medicine at the DHB under the supervision of a senior doctor until November, which is normal procedure to meet Medical Council requirements.
Heath Minister Tony Ryall said through a spokesman that he would not be able to comment on the case as he had no direct role in the hiring of health professionals.
After the Sandy Hook shootings, investigators interviewed Dr Fox by telephone about what he could remember about Lanza, and their report was published this week.