Lafayette Township is one of thirteen townships in Owen County, Indiana, United States. As of the 2020 census, its population was 1,168 (down from 1,207 at 2010) and it contained 562 housing units.
Lafayette Township was organized in 1839.
Moffett-Ralston House was listed on the National Register of Historic Places in 1975.
According to the 2010 census, the township has a total area of , of which (or 99.83%) is land and (or 0.17%) is water.
The township contains these seven cemeteries: Fender, Galimore, Palestine, Saint Walley, Splinter Ridge, Tipton and Wright.