Is there any connection between Lamisil and the onset of Addison's disease?

No there is not

Lamisil (terbinafine hydrochloride) is a prescription medication that is used to treat fingernail or toenail fungus. A new form of Lamisil (oral granules) has also been approved to treat a fungal infection called tinea capitis (also known as ringworm of the scalp).

Treatment

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Treatment for Addison's disease involves replacing the missing cortisol, sometimes in the form of hydrocortisone tablets, or prednisone tablets in a dosing regimen that mimics the physiological concentrations of cortisol. Alternatively one quarter as much prednisolone may be used for equal glucocorticoid effect as hydrocortisone. Treatment must usually be continued for life. In addition, many patients require fludrocortisone as replacement for the missing aldosterone. Caution must be exercised when the person with Addison's disease becomes unwell with infection, has surgery or other trauma, or becomes pregnant. In such instances, their replacement glucocorticoids, whether in the form of hydrocortisone, prednisone, prednisolone, or other equivalent, often need to be increased.

I hope this information is of use to you... besy of luck