Recently, while reading E. Merton Coulter's classic history of antebellum Athens, College Life in the Old South (UGA Press, 1983 reprint), I came across a reference on page 247 to an Athens lynching occurring early in the Civil War. Having checked into the matter, I can now announce that, indeed, there definitely was at least one lynching in Athens prior to 1882. This lynching, possibly but not probably the first lynching in Athens, took place on Wednesday, July 16, 1862.
Wilkes, Donald E. Jr., "A Civil War Lynching in Athens" (2000). Popular Media. Paper 37.