Sorry Joe,
I was just trying to work out the process by which your Catherine would belong to the apparently childless couple, Laurence and Catherine Byrne, but I was obviously missing some steps.
So I take it that the Catherine, born 1849, that we are looking for is Catherine Walker (nee Byrne) and that you have her marriage cert. showing that her father is Laurence Byrne, a tailor.
From the 1881, the mother is Catherine, born about 1823 in Ireland.
Is this correct?