Although stated to have been born in Hanley, the wife of William Lane was born 7/1/1834, bp.2/2/1834 Methodist, Shelton, daughter of William and Hannah.
As you rightly say, the marriage certificate confirms this William is her father.
However, there were indeed 2 Elizabeth Barcroft's and the other ones baptism was 18/1/1835 Hanley, dau. of John and Susanna.
The Elizabeth who married Lewis Lawton consistently gives birth date as ca.1836 and I believe that she was the daughter of John and Susanna. However, only sight of the 1857 marriage certificate can confirm this and, alas, it is not available online.
I can find both Elizabeth's on 1841 census but only the dau. of William in 1851.
Annette