Fayette Township includes Ohio's most southerly point.

It is located in the middle of Lawrence County's Ohio River townships.

Part of South Point, the second-largest municipality in Lawrence County, is located along the downstream shoreline of Fayette Township.

[5] It was named Fayette, in honor of Marquis Lafayette, who was a popular hero of that time and who visited Burlington in 1826.

[6] The township is governed by a three-member board of trustees, who are elected in November of odd-numbered years to a four-year term beginning on the following January 1.