Hi Carole and Giggsycat.
On Henry and Elizabeth's childrens birth certificates, it shows Elizabeth, as late Proudfoot formerly Davies, I cannot find a Proudfoot marriage either. On Henry's death certificate Andrew Lister, son-in law registered his death. One theory is maybe Henry and Elizabeth weren't married. Firstly I cannot find a marriage and secondly Elizabeth on the 1891 census is with Aaron and brother in law, and both herself and Aaron are down as proudfoot. On the marriage for Henry and Lydia, William is down as Henry's father, also Lydia died young.