Lafayette Township was organized in 1858, and named for Gilbert du Motier, Marquis de Lafayette (1757–1834), a French general and American Revolutionary War general.

As of the census[1] of 2000, there were 724 people, 265 households, and 218 families residing in the township.

There were 275 housing units at an average density of 5.5 per square mile (2.1/km2).

The racial makeup of the township was 99.59% White, 0.14% Asian, and 0.28% from two or more races.

14.3% of all households were made up of individuals, and 6.0% had someone living alone who was 65 years of age or older.