Hello Auz,
No doubt in my mind it's the same family. I am named after Thomas Lee. He was my mother's grandfather. Thomas had a number of brothers and sisters. he farmed in a small village named Grandshabeg near Clones. One of Thomas' many brothers was a John Lee, 1849 sounds right too. But i don't know the middle name. Thomas' Father was Francis Lee and his mother was Elizabeth Mckonkey. so i suppose a Mckonkey middle name is more than possible. There are still lot's of Mckonkeys in the area, big farming family over there still. Francis' father was also a John Lee. he married a woman named Anne, or Anna. I'm afraid that's all I know for sure now. The years are fuzzy. Thomas died 1903 or so. Buried in Stonebridge presp cemetery near Grandshabeg, try google maps view. can't see Grandshabeg but you can see the wee church from the roadside view at Stonebridge, east on the monaghan road from Clones. Thomas' two sons came to Canada during the rebellion in 1918. One daughter stayed behind. One of the sons , my grandfather, had children. lot's Lots of Lee boys from him around here in Canada now. I remember Grandfather well. His name was Albert Edward Lee, died 1960 here in Toronto. Francis, his grandfather in the 1860's. John, Francis' father ... unknown dates. The rumour, conjecture really, in the family is that these Lees are descended from a sort of nasty Cromwellian known in some histories as "Ensign William Lee". You may want to Google him up. Of some interest, I suppose, is that while I have fond memories of grandfather, he and his inlaws, among whom were, coincidentally, some Halls, were all virulently anti-Catholic. I wonder what he would have though of me marrying a Jewish woman. Writing about lineages etc is tough isn't it. Good luck hunting.
As your in Auz there is another Lee connected name that seems to only exist down there these days, ie Teasey or Teacy. regards from Toronto.
Tom Johnston