It is circumstantial but Eleanor became a bookbinder, as did Lewis. James did not so he seems to stand apart from "father" Edward the bookbinder.
Also Eleanor was born Hull. Lewis born York. My guess is that Edwards first wife died in York after she gave birth to Lewis then he married Elizabeth who brought along James.
Dave

Here is Edwards first marriage in St Helen, York 25th June 1826 (FMP)
Edward Dunn, BOOKBINDER and a bachelor married Mary Swinbank, Spinster.
Dave

Hi all

Theres a baptism for;

16 Oct 1831 for a James Carter, illegitimate son of (no forename) Carter, Spinster, a servant of Farlington nr York ???

Denise

Great find Denise.
Below sequenceThis seems to fit well for the mother of Eleanor Dunn (abt 1829 Hull) and Lewis Dunn (abt 1832 York):

Mary Ann Swinback bap 1794 York
1826 York Edward Dunn married Mary Swinback
27 March 1834 Mary Ann Dunn buried York age 38
19th Nov 1834 Edward Dunn (widower) married Elizabeth Carter

Dave