Just as a comment: neuroborreliosis is a definite organic cause of depression, though it is easiest to determine this at autopsy. This can be described as a neurological complication of Lyme disease.
However, I would not consider IVIG as a general treatment for "depression", except on an experimental basis to determine if there is an underlying physiological problem. The problem is that "depression" is a very broad diagnostic category which has absolutely no connection with particular etiologies.
Here is something I had already written offline when this thread started:
A diagnostic category like major depressive disorder may be the result of a wide variety of pathological physiological conditions: direct brain trauma, subdural hematoma, viral encephalitis, seizure disorders, influenza, cardiovascular disease, MS, SLE, pulmonary conditions, liver impairment caused by hepatitis C, undetected cancer, etc.
During the era of patent medicines most treatments for "depression" which rapidly relieved symptoms contained
substances which are now controlled by the DEA. (You might also check on treatments for sleep disorders, including codeine and morphine.) This should be enough to make one cautious about using this particular symptom as a diagnostic category. Legitimate antidepressants all have the problem that the side effects appear before the benefits. Misunderstanding of this by clinicians often leads to avoidable suicides.
This is very far from saying that IVIG and/or minocycline have no place in the treatment of depression. Some causes of depression do respond to these treatments. Unfortunately, this will not help at all if the organic cause is cardiovascular disease or subdural hematoma. A thorough search for treatable etiology is necessary to deal with this. If this were regularly done it would save lives, and also destroy the convenience and economics of dumping patients in a diagnostic category based on a single symptom.