Firstly, thank you all for your replies. This is what I can tell you about my great great grandfather. From what I know he was born in St. Jarlath, Tuam, although this is just from another profile on Ancestry, they have his date of birth as 1867, which backs up what you have pointed out about fluidity of birth dates. Patrick joined the Connaught Rangers at the outbreak of WW1 and was killed at Gallipoli on August 23, 1915. His name is on the Cenotaph in Birkenhead.
Now on his wedding banns, in Liverpool in 1897 ( married a Protestant Liverpool girl in C of E church around the corner from my beloved Anfield, but the children were baptised and raised as catholics) his father is given as Martin, occupation farmer, deceased. Apparently, he had an older brother called John, he was the second born and his youngest brother is called Martin. Going on the naming traditions, would it be safe to say that as he was the second born, would his maternal grandfather be Patrick? I do not know of any sisters, but that does not mean they do not exist. There is a baptism record from 1855 for a John Lyons, parents Martin and Catherine Lyons from Tuam, but would the distance in the ages be too great?
Now the Bridget link does interest me because could a sister have slipped the net? The youngest son Martin, named one of his children Bridget.
Now Patrick named his children in order, Catherine, Martin ( my great grandfather), Martha, Patrick and John Dennis. Catherine and Martin were born in Liverpool, shortly after, the family moved across the Mersey and Martha, Patrick and John Dennis were born in Birkenhead, where I am now.
Based on the info that you have all kindly given me, I have new lines I can toy with, so once again, thank you very much. If I may ask one other question, based on my family background would the present members of my family be considered as part of the extended Irish diaspora? Although gone a long time, Patrick didn't exactly go far and Merseyside cherishes its Irish connection in the same way parts of the N.E. USA do. I hope that I have phrased that question properly, and it doesn't come across as cultural appropriation. I have a firm identity of my own, rooted in our peculiar view of ourselves as opposed to the rest of England that we have here, but the deeper I delve it's important for me to know more.
Take care
Michael