They talk of a boy who dressed smartly and worked hard, but who barely said a word during his time at school.
Police officers have said he may have had a personality or developmental disorder, while one relative told ABC News he was "obviously not well".
Lanza appears to have kept a low profile throughout his life. US media report that unusually, his high school yearbook of 2010 contained no photograph of him.
"Camera shy" was the comment by his entry.
Unlike the majority of his peers, Lanza apparently had no Facebook page. His online footprint was minimal. He appears not to have been known to the police.
Adam Lanza lived with his mother in a well-to-do neighbourhood of Newtown, Connecticut. The house is about five miles (8km) from Sandy Hook School, which he attended as a child.
He went on to Newtown High School, but made few friends. His mother pulled him out of the school and taught him at home because she was unhappy with the school district's plan for his education.
His aunt, Marsha Lanza, said that Adam was "definitely the challenge to the family in that house".
"Every family has one. I have one. They have one. â€¦ But he was a very bright boy, he was smart," she said.
Intelligent but shy and nervous were the most common memories of those who learnt beside him.
Richard Novia, who was head of security at Newtown High School, said it was clear Lanza had "some disabilities".
He was protective of his personal space and sometimes appeared to completely withdraw into himself or to "take flight", Mr Novia told AP, meaning his mother had to be called in to resolve the problem.
"You had yourself a very scared young boy, who was very nervous around people he could trust or he refused to speak with."
Mr Novia helped to run a technology club, which Lanza attended, and said he had to keep a close eye on him while the club was using soldering equipment or electrical equipment.
"If that boy would've burned himself, he would not have known it or felt it physically," he said.
An inability to respond to sensation, and a difficult in relating to other people, could be an indication of Asperger's Syndrome (a form of autism), say experts.
They stress there is no direct link between the condition and aggression. People with the condition can sometimes struggle to express themselves in socially expected ways, however.
Olivia DeVivo was a student with Lanza in the 10th grade, at about the age of 15. She told the Associated Press he was "very shy and didn't make an effort to interact with anybody".
"Now looking back, it's kind of like 'OK, he had all these signs,' but you can't say every shy person would do something like this," she said.
A former school bus driver in the town, Marsha Moskowitz, said she remembered the Lanza boys.
"You know the trouble kids, and you figure, 'Pfft, that one's going to be trouble.' But I never would have thought that about them," she told the Hartford Courant newspaper.
Marsha Lanza told the Associated Press that Adam had been raised by kind, nurturing parents, who would not have hesitated to seek counselling for their son if he needed it.
The parents divorced in 2009, having separated at least three years earlier. His father, Peter Lanza, moved to Stamford, Connecticut, and recently remarried.
His mother, Nancy, remained in the family home, where it is thought she was killed by her son. She had previously worked in finance, but her divorce settlement left her well off and she stayed at home.
Friends said she was popular and sociable. An acquaintance, Jim Leff, wrote on his blog that she was "a friend-of-friends who I periodically would briefly bump into, and who always seemed kind-hearted... and, yes, a bit high-strung. But with ample reason, as it turns out."
Contrary to initial reports, Nancy Lanza never worked as a teacher at Sandy Hook Elementary School.
She was a gun enthusiast who is reported to have taken her sons with her to the shooting range. Adam Lanza used her legally purchased Bushmaster assault rifle to carry out his attack. He was also carrying his mother's two handguns, a Glock pistol and a Sig Sauer. Police found a shotgun in his car.
Adam Lanza's elder brother, 24-year-old Ryan, who was initially named in the media as the suspected gunman, has been helping police with their investigation. US media is reporting that he told them he had had no contact with his brother since 2010.
In a statement issued to the media, Lanza's father said: "No words can truly express how heartbroken we are.
"We, too, are asking why. Like so many of you, we are saddened and struggling to make sense of what has transpired."
Former classmates of Adam Lanza, 20, the man identified as the gunman in the Sandy Hook School killings, do not remember much about him.