Wow! I've been doing errands while the replies accumulated.
I think you have revealed the main thing I hoped to find out from a gravestone, if someone knew what was meant by the family burying-ground and someone found a grave with a helpful inscription: namely the maiden name of the wife of Henry McLorinan, who died at Castle Street Antrim in 1875. It was already established that the Rev. Thomas McLorinan was uncle of Lizzie, daughter of John McDowell (died Antrim 1886), who was almost certainly a son-in-law of Henry McLorinan. So Thomas was a son of Henry McLorinan, and the mother you have found for him, born Martha Mackey, was Henry McLorinan's wife, mother-in-law of John McDowell.
I haven't found a record of her death. Maybe it didn't get a civil record, as seems to have been the case with her son Thomas McLorinan. Or maybe it was before civil records started.
I had looked for Martha McLorinan as a daughter of Henry McL, because the Valuation Revision Books for 1867-1881 have a house on Castle Street with Henry McLorinan crossed out and replaced by Martha, presumably when Henry died. And I had found the death of Martha McL, spinster, and noted that it was reported by John Simpson, whose marriage (if it's the same person) to Mary McL I had found, tentatively identifying Mary as a daughter of "my" Henry. About Martha, I was given pause by her father being described as a shopkeeper, not a farmer. And come to think of it, what is the profession of Mary's father on that marriage certificate? Kiltaglassan's enhancement doesn't make that end of the certificate much clearer; might it actually be grocer, not farmer as I was assuming? There was a grocer (and haberdasher) Henry McLorinan on Main Street Antrim in 1870 (also the Misses McLorinan, haberdashers; daughters?), and I had thought that must be a different Henry McLorinan. Is it possible that one person was called a farmer in some records and a grocer/shopkeeper in others?
I had found Alexander Mackey on the list of Methodist ministers in Ireland when I was looking for more on Thomas McLorinan, and the name intrigued me for a quite other reason. I have been interested in finding a Thomas Parker for John McDowell's eldest son to be named after. (The first two, Thomas Parker McD and Henry McLorinan McD, used all three names in many contexts. The youngest, John junior, seems to have been just John. Having a middle name seems to have been significant.) Now Henry McLorinan McD had a friend Alexander Mackey Parker (born Antrim 1841), who was a witness at Henry's marriage and later the father-in-law of Henry's daughter Elizabeth. The Rev. Alexander Mackey, a bachelor, wasn't anyone's father-in-law, but perhaps Alexander Mackey Parker was named after a charismatic preacher, as was also apparently not uncommon. I can't resist adding that Lizzie McDowell Stewart's youngest son, so a nephew of Henry McL McD, was called Alex Parker Stewart, according to the 1901 census.
I would still be interested in knowing if anyone knows what was meant by the family burying-ground!
There's a lot else that's intriguing in what you have uncovered. For instance, was Samuel Johnson, father-in-law of John McDowell junior and eponym of his son Samuel Johnson McDowell, a descendant of Mary Mackey and William Johnson? But even without raising new questions, there's plenty for me to digest. Many thanks.
