Lafayette Township is a township in Story County, Iowa, USA.

Lafayette Township covers an area of 35.8 square miles (93 km2) and contains the incorporated town of Story City.

According to the USGS, it contains three cemeteries: Fairview Cemetery, Sowers Cemetery and South Saint Petri Cemetery.

U.S. Route 69 runs north and south through the township and County Roads E18 and E15 run east–west.

This article about the geography of Story County, Iowa is a stub.