Donacavey, meaning Church of the hollow, derives its name from the site of the first church in the area, believed to have been founded by St. Patrick. Ruins of a later church on this site and the adjoining disused cemetery are all that remain today. Earliest references to a Catholic place of worship in Fintona in the post-Reformation era are found in the Popery Report of 1731, which mentions there being a masshouse in existence before the reign of George I, which began in 1714.

Today the parish has one large church, situated less than a mile from Fintona town, in the townland of Lisnabulreavy. This present church was completed in 1841 and is dedicated to St. Lawrence, martyred for his faith at Rome in 258, whose feastday is on 10 August. The church is built from local sandstone and the roof timbers are memel, which local parishioners transported from Ballyshannon.

Over the years, the church had undegone several renovations including the building of the tower and spire in 1872 and major work in 1924-1927. Then in 1996 the sanctury was re-organised and the church extended t include avcillary rooms and a chapel for morning Mass, dedicated to Our Lady.

Two notable natives of Donacavey were Edward Maginn, Bishop of Derry (died 1848) and James Joseph McNamee, Bishop of Ardagh and Clonmacnois (died 1966), known in his time as the Golden Voice of the Irish Catholic hierarchy.