The Old City Courthouse. Built in 1764 as a courthouse. Subsequently used as a school. It is now a community hall.
Other records say the City Court House was built in 1761, not 1764. See the section 'MODERN LIMERICK. 125' in this archived book 'Limerick And Its Sieges' by Rev. James Dowd, A.B., LCD (2nd Edition 1890): http://www.archive.org/stream/limerickitssiege00dowd/limerickitssiege00dowd_djvu.txt