Elizabeth Lloyd was born 16 Nov 1837 with "Henry Claton, porter" named as father on her birth certificate. Her birth is indexed as "Elizabeth Claton". She appears in Bala in the 1841 census living with her grandparents as Elizabeth Lloyd, and on her marriage certificate in 1861 puts her father down as "Henry Lloyd, butcher, deceased". There is no reason to doubt the birth certificate that Henry Claton (or some rendering of this name) was the father of Elizabeth Lloyd, but she lived her whole life as Elizabeth Lloyd, and her mother Bridget Lloyd never married Henry Claton. The birth certificate oddly does not give the place of birth. He may have died or it could be the shoemaker from Welshpool. Montgomery District includes Pool, and there are no Clayton or Claton deaths in Merioneth (ie Bala).
Elizabeth Lloyd's place of birth is recorded as Llangollen in all the censuses through her life, so one assumes that she was born there, and that is where her parents Bridget Lloyd and Henry Claton met.
There appear to be only two possibilities for his identity, either he died between the conception of Elizabeth Lloyd in 1837 and the census in 1841, or he is Henry Clayton of Welshpool that one can follow through the censuses below.
The only deaths that it could have been for a Henry Clayton in North Wales at that time are Deaths Dec 1838 Clayton Henry Montgomery 27 71 (not him, he was only 12 when he died) or Deaths Jun 1839 Clayton Henry Montgomery 27 80 (not him, a 53 year old innkeeper).
If he did not die, then the only other possibility is that he is Henry Clayton, shoemaker of Welshpool, who can be seen in the censuses of 1841, 1851, 1861, 1871, 1881 and 1891 before expiring in the workhouse in 1893. This Henry Clayton lives in and around Welshpool except for a foray to Thurstaston, Cheshire in 1881, which appears to have been to "baby sit" for his grandson. He does not marry, but has a son Henry born circa 1838, about a year after Elizabeth Lloyd was born.
Henry Claton, age 35, shoemaker & lodger, born Welshpool, with 13 year old son living at Welshpool. No wife & down as unmarried
Henry Clayton, shoemaker & boarder age 46. Living at Welshpool, & born Welshpool
Henry Clayton, age 56 and widower, bootmaker, lodger, born in Welshpool and living in Welshpool.
Living with George Clayton, grandson at Civil Parish: Thurstaston, Cheshire
In the Forden Union Workhouse
Name: Henry Clayton
Estimated Birth Year: about 1814
Year of Registration: Jul-Aug-Sep, 1893
Age at Death: 79
District: Forden, Montgomeryshire, Shropshire
Volume: 11b. Page: 123
Bridget Lloyd 1811