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I searched for civil birth records for Patrick Lloyd from 1890-1915 and although there were records, none had the parents you listed. I also searched on Roots Ireland with no success. I found no records for any children of Richard Lloyd and Annie McKenzie.
I checked the 1911 census for Mary Keogh in Co. Dublin. There were 236 Mary Keoghs.I did not see Brighton Gardens but saw a record on Brighton Avenue.