In the IGI Pilot database there is 1 record for the death of Eliza Winterscale:
Name: Eliza Winterscale
Registration district: Sligo
Record type: DEATHS
Registration date - quarter and year: Oct - Dec 1880
Estimated birth year: 1790
Film number: 101590
Digital GS number: 4200672
Image number: 00311
Collection: Ireland, Civil Registration Indexes 1845-1958
This would be the (spinster) sister of John Winterscale judging from the birth date around the same time & I suppose the mother Eliza Winterscale died much earlier & so is not in this collection. Apparently this index can be used to get the original certificate from the GRO in Ireland but (from the examples) it appears their death certificates don't give any parent detail anyway.
As for James Winterscale Esq, yes I came across a Google book entry which referred to him being a signatory on a petition which was part of some debate in parliament (just google James Winterscale & its about the 4th entry), so he appears to have been quite notable.