Edward Laurenson

patm, 

John Grenham says that Lawrenson and variants is rare in Ireland, but was found in Belfast and is of Scottish or English origins. Given this background and the fact that the family were apparently Church of Ireland, the normal inference is that they moved to Ireland in the 1600s, perhaps as part of the Plantation or perhaps following Cromwell’s rather notorious visit when some of his  troops were awarded land in return for their services. There are few records of individual Plantation settlers save for a few major landowners.

https://www.johngrenham.com/surnames/

One place where the surname is very common today is the Shetland Islands, though that would be an unusual part of Britain for a conventional Plantation family to have originated. Lawrenson, in Shetland, is a Norse name. The Norse occupied Shetland & Orkney in the 8^th & 9^th centuries and many surnames there are consequently of Norse patronymic origin. Shetland & Orkney were annexed to Scotland, from Denmark & Norway (at that time one country) in the 1400s, as part of a Royal dowry.

My guide to Church of Ireland records says that the baptism and burial records for Durrow start in 1706/7 and marriages in 1797. It also says that rootsireland has coverage of some years (it doesn’t say which). The original records are now held in the RCB Library in Dublin. (Personal visit required to access them). There is a slow project to put all the records on-line in due course.

https://www.ireland.anglican.org/news/rcb-library-notes

It is rare with Irish research to get back much earlier than 1800. Most research comes to a stop at that point due to the general lack of records.

If Robert Laurenson was in the tithes then that indicates he was almost certainly a farmer. It’s possible that he might be in the Registry of Deeds records (on Familysearch) which start in 1709. You might find a lease or two there for the family.