[1] La Moille Township was named after the Lamoille River valley in Vermont.

There were 475 housing units at an average density of 12.61 per square mile (4.87/km2).

The racial makeup of the township was 93.47% White, 0.20% African American, 0.40% Native American, 0.20% Asian, 0.10% Pacific Islander, 0.69% from other races, and 4.95% from two or more races.

There were 430 households, out of which 26.70% had children under the age of 18 living with them, 60.47% were married couples living together, 4.65% had a female householder with no spouse present, and 33.26% were non-families.

26.70% of all households were made up of individuals, and 13.50% had someone living alone who was 65 years of age or older.