I may share part of your line. If ours are the same, Armstrong Thomas Lyster (the 1st) had a brother, William Narcissus Lyster, who became an Episcopal priest and eventually ended up in Michigan, where he is buried. The one discrepancy I have is that my information lists the father of William Narcissus and Armstrong Thomas as William H. Lyster, not William John Lyster. My information as to the elder William's name comes from the Michigan Genealogical Death Index record of the death of William Narcissus Lyster, which are transcribed from handwritten files, so a misprint or typo is entirely possible.
My information is: William (H?) Lyster married Martha ?? -2 sons (at least) Armstrong Thomas Lyster (b. 1803, County Wexford) William Narcissus Lyster (b. 5 Mar 1805, Co Wexford. d. 9 Sep 1877, Columbia, Michigan)
The Rev. William Narcissus Lyster married Ellen Emily ?? (b. 19 Feb 1811, Birch Grove, Co Wexford. d. 27 Sep 1861, Georgetown, Disctrict of Columbia [from her gravemarker, Detroit, MI]) -William and Emily had 2 children (at least) Henry Francis LeHunte Lyster (b. 8 Nov 1837, Saunderscourt, Co Wexford. d. 3 Oct 1894, Detroit, MI) Bessie Lyster (b. 1846. d. 8 Oct 1870, Denver, Colorado)
Henry F.L. Lyster married Winifred Lee Brent (1842-1930). -7 children William John LeHunte Lyster (1869-1947) Lizzie G. Lyster (1869-1873) Eleanor Carroll Lyster (1871-1924) Bessie Lyster (1871-1876) Henry Laurence Lyster (1873-1948) Florence Murray Lyster (1875-?) Thomas Lee Brent Lyster (1878-1949)
Eleanor Carroll Lyster married Edward Horatio Parker (1865-1913). -3 children Thomas Maxwell Parker (1897-1942) Henry Lyster Parker (1899-?) Edward Carroll Parker (1902-1977)
Edward Carroll Parker married Mary Deming (1906-1999) -2 children Helen Parker (1931-1999) Edward Carroll Parker, Jr (b. 1935)
Edward Carroll Parker, Jr married Lynda Helen Deming (b. 1943) -2 children Charles Carroll Parker [me] Edward Sherman Parker
I'm afraid I can't offer any additional information beyond the elder William Lyster of County Wexford, but it appears your research in that area is well ahead of mine. If you can either confirm or deny the relation between my William Narcissus Lyster and your Armstrong Thomas Lyster, I would appreciate it. You can view more complete information on my genealogical research at my site: http://geocities.com/parkers_01/http://geocities.com/parkers_01/