Ron,
The names Stewart & Stuart are interchangeable in Ireland and it’s common to see spelling switch between the two. There are numerous names like that with multiple spelling options. Folk then weren’t bothered about the idea of a single “correct” form which modern officialdom prefers.
Looking at the records you have found for the property in Lisnawery, I see that Margaret Scott was the occupant at the time of Griffiths Valuation in 1860. So her husband had died before that. The property remains in her name till 1881 when it changes to John. That suggests she has died, and there is a death for her at Lisnawery on 31.7.1880 aged 82. Farmer’s widow. Informant was John. He might be her son. Certainly he acquired the property after her death.
https://civilrecords.irishgenealogy.ie/churchrecords/images/deaths_returns/deaths_1880/06466/4859467.pdf
Stewart Scott was born at Lisnawery on 6th Aug 1866 to John Scott and Rachel Martin. John & Rachel married 22.1.1853 at Clogher Cathedral. (His father was Stewart Scott farmer). Rachel Scott died 9.5.1898 aged 68. Informant was her son Stewart.
John’s name remains as tenant until 1904. Again that suggests he may have died. There is a death for him at Lisnawery on 28.5.1900 aged 78. Farmer & widower. Informant was his son Stewart. So the property passed to Stewart who is there in the 1901 census. The property remains in Stewart’s name until 1929 (which is when those records stop) but he isn’t there in the 1911 census. Instead he has sublet to a William Walker. (You can find that out by exploring the house and building return on the census).
http://www.census.nationalarchives.ie/pages/1911/Tyrone/Favor_Royal/Lisnawery/855035/
I don't see Stewart Scott in Ireland in the 1911 census, which suggests he had left Ireland. (You might want to search the 1911 Scottish & English censuses.). I looked for a marriage for him 1901 to 1921 in Ireland but did not see one. Alexander Scott had died 22.2.1908 at Lisnawery. I suspect that Stewart didn’t feel like running the farm on his own, and left.
Statutory birth registration only started in Ireland in 1864. Prior to that you need to rely on church records. The Scott family were Church of Ireland (in the 1901 census anyway). So you probably need to search Errigal Keerogue's records. They start in 1812 and there’s a copy in PRONI in Belfast. Hopefully you may find your Robert’s baptism as well as any other siblings. And you might find Stewart's marriage and burial.
The farm usually went to the eldest son, leaving other sons to make their own way in the world. So you may find John Scott is Robert’s elder brother.
Regarding where the family originated, Scott is not a native Irish surname. Given that the family was Church of Ireland, lived in Co Tyrone and had an essentially Scottish surname, then it’s likely that they originated in Scotland. (Tyrone was heavily settled by Scots). However the main migration of Scots to Ireland was in the 1600s when some 200,000 are estimated to have arrived (something like 20% of the entire Scottish population). Some came as part of the Plantation in the early 1600s, others throughout the 1600s for various reasons and then there was a big influx in the 1690s due to famine in Scotland. By the 1700s and 1800s they were leaving again. Some may have arrived then but the general trend was outwards. So your family probably arrived in the 1600s. However there are no records of the individuals who arrived then and no real way of tracing in detail where they came from in Scotland. They mostly came from the Lowlands & Southern Uplands, we know that. Highlanders weren’t much attracted to lowland farming in Ireland, and weren’t encouraged to come either as their loyalty to the Crown was a bit suspect at times. But beyond that generalization it’s not normally possible to say where someone originated in Scotland.
