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My maternal great grandmother was Sarah Warmington from Tullyvallen who married John Bailie.
I remember from my research that there is another Sarah Warmington from Tullyvallen about the same age but not related to me ( I think)
I also have McGaw/ Megaw/Megaw on my paternal side but from Skerrif townland , still in the same general area.

you don't say what cemeteries you have searched and I'm not sure how much you know about the history of Lurgan and this is just a thought, but the existing Lurgan Hospital which is close to Union St and Mark street was originally a Workhouse and in the 1840s it also included a 40 bedded Fever Hospital ( you mentioned your relative died of TB ) . the dead were buried in an adjacent graveyard.
Lurgan & Portadown District Hospital didn't open until 1929 so the Fever Hospital might have been still operating when your family member died.

have you tried looking on the creggan historical society web site. if you search the townlands section for the townlands you have mentioned, there are several McMahons mentioned, the oldest being Hugh McMahon.

yes . I came across an article in the Newry Reporter about Loyalism in The Fews ( South Armagh ) where I read that my Grandmother Anna and her sister walked from Crossmaglen to Newtownhamilton to sign The Ulster Covenant .She would have been 17yrs at the time and her sister 19yrs.

Hi, I also think it is Tullyvallen.
My paternal grt grandmother was Amelia Megaw/ McGaw  from townland of Skerriff  Parish of Newtownhamilton which is the adjoining townland to Tullyvallen where my mother's family are from. Both townlands in Co Armagh but registration district for my Megaws was Castleblaney.
Have a look at The Creggan History Society site if you haven't already done so. Great information.