Lafayette Township is one of the twenty-two townships of Coshocton County, Ohio, United States. The 2020 census reported 4,250 people living in the township.

Coshocton County is a county located in the U.S. state of Ohio. As of the 2020 census, the population was 36,612. Its county seat and largest city is Coshocton. The county lies within the Appalachian region of the state. The county was formed on January 31, 1810, from portions of Muskingum and Tuscarawas Counties and later organized in 1811. Its name comes from the Delaware Indian language and has been translated as "union of waters" or "black bear crossing". Coshocton was mentioned by David Zeisberger in his diary from the 1780s using the German spelling "Goschachgünk". The Coshocton, OH Micropolitan Statistical Area includes all of Coshocton County.