I think we can safely rule out Fragile-X Syndrome, because a report by the Office of the Child Advocate in Connecticut in November 2014 stated that Lanza suffered from anorexia as a teenager. The authors wrote that "Anorexia can produce cognitive impairment and it is likely that anorexia combined with an autism spectrum disorder and OCD compounded Lanza's risk for suicide". They also noted that at the time of his death, Lanza was anorexic (six feet tall and 112 pounds), to the point of malnutrition and resultant brain damage. Anorexia would fully explain his "Lean and Hungry" appearance, as well.
Source (PDF): Shooting At Sandy Hook Elementary School.
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