From familysearch, rental records,and elsewhere there was an Abram who died 1758 in the area and Mary Lunn d 1766, so the name is fairly old there.
As far as I can unravel:
Abraham b 1768 d 1837 @69 had son Matthew b 1802 d 1876 who married Eleanor Orr b 1810 d 1886.Abraham was married to Mary and had also had sons Hugh b 1793, Edward b 1790 and George b 1795 assuming there was one Abraham.
From the taxation of rentals, there was an Edward who married Helena and had Wm as a brother and James as a son.Following the house rentals, James takes over from Edward between 1866 and 1878 and Wm takes over from him between 1879 and 1888 to be replaced by Thomas Lunn 1888-1901 This may be the Thomas who died 1901. This Edward seems to be the same person as James who married Helena, so perhaps I read the rentals incorrectly or ??
Matthew and Eleanor had Abraham b 1841, Helena b 1840 d 1918?, William of Clankil... m. Mary Crossey and Jane Mitchell, Elizabeth b 1843, Margaret b 1836 died, Margaret Ann b 1850 d 1851, Edward b 1854 and Ellen b 1839 who may be known as Helena. She may be the lady who is the widowed niece of Margaret Seyton in 1901 as her age looks right.
Abraham of Ballymacateerd 1890 and mentions sister Helen Lunn and chose Wm of Clankil...?as executorWhen Abraham died, a Wm Lunn took over the rent, but not for long.
A Helena Lunn married James Lunn b. 1829 d 1878 of Lurgan in 1876 and were said to be not closely related. James had brother Wm who appears to have inheritted the estate in Ballymacateer.
The will of Wm of Clankil...with farm in Ballymacateer d. 1900 says Mary Crossey bore him sons James b 1881, Edward b 1881, Thomas b 1868, Elizabeth 1876, and Ellen (eleanor) b 1878.Jane Mitchell bore him Wm. who lives near Gillhall, Co Down. Thomas appears to died 1901 and lists survivors as James, Edward, Ellen and Lizzie
Probably related is Matthew who married Jane Rennix and had sons Matthew 1834 and Hugh 1832.
Also probably related was another Edward Lunnb 1773 d 1861 who married Margaret b 1787 d 1822 This Edmund had the seat #21 in 1792 in the parish church and perhaps contributed 5 pounds in 1835. After his wife died he married Ellen Swenarton b 1788. Children were William b 1825, James b 1929. This appears to be the James that married Helena Lunn.
John Lunn m. Mary doesn't appear to share many given names.He has children Robert b 1827 m Jane Hamilton 1855, John b 1826 m Elizabeth Hamilton 1852, William b 1840 m. Mary Whiteside 1862, Henry b 1830, Jane b 1844, & 1833, Christiana b 1846 and Mary Ann b 1838 ,m John West and Alice m. Wm Hill 1860.William Hill and Alice had children John, Jane, Elizabeth in Moira, Robert Lunn and Jane had children Mary 1867, Elizabeth abt 1871, Robert 1870, William 1872 and Joseph 1874. They are on Hamilton St in Lurgan in 1901 with their nephew Robert Lyness, son of Ellen Lunn and James Lyness.Ellen probably was born 1863 and may be on George's St.
John and Elizabeth Hamilton Lunn had Joseph Henry.He ison Hill Street in 1911 and with parents there in 1901.
I don't know if there were more children, but I expect so.Also the earlier dates are from baptisms or death ages and may be off some.