From the Wikipedia page 
Willisau District is one of the five districts (German: Ämter), of the German-speaking Canton of Lucerne, Switzerland. Its capital is the town of Willisau. It has a population of 53,317 (as of 31 December 2016). In 2013 the name was changed from Amt Willisau to Wahlkreis Willisau as part of a reorganization of the Canton. A sixth Wahlkreis was created, but in Willisau everything else remained essentially unchanged.
Municipalities listed on the Wikipedia page