I think that legal documents in the form of the Lanza's 2009 divorce settlement are a solid source. Mediator Paula Levy worked closely with the Lanza's when going through divorce in order to reach an agreement on the terms of settlement.
According to the Huffington Post:
The key takeaways from the Lanza's divorce documents:
1. They informed an officer of the Court that their son was diagnosed with Asperger's syndrome.
2. They were in agreement about this fact: "the Lanzas were in complete agreement on how to address Adam's needs and said little about the details of his condition." Frankly if the parents didn't agree that their son had Asperger's syndrome or how they would approach treatment, this would be an issue in a divorce.
3. The mediator states the Lanza's were "equally concerned about their son's needs." And, "They worked together about it."
Therefore, in both divorce settlement documents and comments to an officer of the Court the Lanza's agreed that their son was diagnosed with Asperger's syndrome.
That being said, anyone who has known or loved someone diagnosed with Asperger's syndrome understands that there is ZERO correlation between the horrific actions of the Newtown shooter and individuals diagnosed with Asperger's syndrome.