In the beginning of the 18th century ( ca 1718 ) the French ( Napoleon ) forced all Dutch to take on a surname, in many cases children from one family took on different surnames, in the case of the children of Waling Yedes and Wytske Keimpes this resulted in multiple surnames, Dijkstra / Leistra / Leystra ( later also named van der Leij or van der Ley ).
The first known "Leijstra" is Freerk Walings
Since the livingplace of this family was close to the village of Place:Oude Leije, Het Bildt, Friesland, Netherlands, but also on a 'Dijk' both surnames make sence and give a indication where they lived and felt at home. 'Leije' is old Frisian for a 'lock'(dutch : Sluis), the placename Alde Leije refers to the old lock in the village from the times it was nearby the Frisian coast.
Eventhough 'Dijkstra' is by far more common, and has multiple origins compared to 'van der Ley', even today both names are most common in and arround the place of origin, see images below :
The farm called "Balk-end" nearby the Balkendsterpolder is known as the livingplace of the firstknown "van der Ley's", although this farm is no older then 1840.