I'm absolutely baffled by this family. James Byrne was a young lad who lived with his mother in 31 Lower Stephen Street, Dublin in 1916.
Margaret Byrne, who's variously described as "dull-witted" and "mentally deficient" later lived in 34 or 36 Clarendon Street. I've found a marriage registration that may be hers - in Dublin, in 1887, when Patrick Byrne married Margaret Daly. Patrick, a gardener, was living in 33 1/2 Clarendon Street, and Margaret in St Michael's, Eglinton Road. Neither Thom's nor the census is any help in saying what St Michael's may have been.
I've also found Margaret's and James's death registrations (attached). (I notice that the registrar has corrected Margaret's name to Martha…? But if the marriage registration is her, then she married as Margaret, and she's Margaret in the Military Archives pension records.
However, I've failed to find Margaret and James (most inconsiderately, not only using the commonest surname in Dublin but also two of the commonest names) in birth records or in either of the censuses. And I haven't found Patrick's death registration - Margaret was a widow when her son died.
Unless… could this Martha be her? And if so, did her other son die? The census entry seems confused.
https://www.census.nationalarchives.ie/pages/1911/Dublin/Mansion_House/Mercer_Street__Upper/74217/But still no sign of them in 1901…