It was not obligatory, so is rather hit or miss. It starts in 1708. The first Fulton in Lisburn to be recorded in the Rgistry is James in 1740, presumably the one on the rent roll of 1728, as he is again associated with the name Coulson. Belfast Newsletter . Originals in Linenhall Library Belfast.
Microfilms are available in several locations.
This is one of the oldest newspapers in the world which is still in publication and with the exception of a very few individual copies the collection exists complete from 1734. There is a full index of the paper up to 1800 and an index births, marriages, and deaths up to about 1864 after which those facts can be found in the General Registry. I can really recommend this site which is much easier to use than the microfiche of the index which I have used in the past. The Map shows the parishes of Co. Antrim lying in the vicinity of Lisburn. I have also sketched the position of the adjoining Co.