I tried death registrations of Luke Brennan in case informant gave that name instead of Thomas.
Only 2 in 1909. Roscommon Superintendent Registry District, aged 86, widower, informant son Charlie. The other was in County Monaghan.
1907 Roscommon S.R. District, age 69, labourer, died in workhouse.
1908 Roscommon S.R. District age 75, wodower, informant was son, David.
1911 Tobbercurry , County Sligo, aged 80, farmer, informant Mary Brennan, widow of deceased.
I even searched under Ludovich as a surname in case there was a wrong transcription. I doubt if "Ludovich" would have been used in Ireland; there were enough problems trying to spell native Irish names.
I had no luck with birth registration of son Luke either. I searched 1864 (start of civil registration of births)-1875.
There were 2 in 1871 :
Boyle S.R. District with parents Luke & Maria;
Athlone S.R. district, parents Luke & Mary (Kelly)
1868 Roscommon S.R. District, parents Luke & Marie
Luke births with a father called Thomas:
1864 Tubbercurry S.R. District, parents Thomas & Atty
1869 Roscommon S.R. District, parents Thomas & Mary Anne (Gilleran)
Interestingly most Luke Brennan births during that period were in counties Roscommon and Sligo.
Luke , the son may have been registered under a different first name or his parents didn't register him, or he may heve been older than you think and born before civil registration, or not born in Ireland,
Do you know if Mary Ann married? Have you searched for her on 1901 and 1911 census as Mary or Mary Ann Brennan and for death registration 1930s & 1940s?
Do you know what happened to Luke, Patrick and Thomas junior?