Charles Andrew Williams: Survived the shooting and was not diagnosed with anything during the trial, at least to my knowledge.
Mitchell Johnson & Andrew Golden: Survived their shooting. Because of their age, their psychiatric examination was not made public. According to the book "Rampage. The social roots of school shootings", there were people who had access to this reports and commented, that there was no major disorder or illness noted in the examination.
T.J. Lane: Survived his shooting. He was not diagnosed with anything during the trial, at least to my knowledge.
To be honest, that are all cases, in which a shooter did not seem to suffer from a personality disorder or a mental illness, that I know of.
Hence, it is hard for me to believe, that mental illnesses among mass shooters are "rarely" the case.