What a sleuth you are, ciderdrinker! It took me months to assemble that lot ... though I wasn't sure Eleanor's baptism was her - as you say, there don't seem to be records for their other children. I wonder if Elizabeth Lucas was her aunt? I can't seem to find out much about the Lucas family; they might be the Catholics, I suppose. And although Bate seems to be a very common surname in Wolverhampton, my John William says he was born in London.
(In the 1841 census, I did wonder if Mary Williams actually belonged to the previous entry, which is for a Thomas Williams?)
William Lacon, carpenter, was my great grandfather. His daughter Jane married Joseph Morrison, who was her aunt Maria Victoria's brother-in-law!
Everything I've discovered about the Bates and Lacons is on ancestry.co.uk. Do you have a family, or a local, connection? Let me know if you want an invite to my tree.
Thanks for the suggestion of local papers for anything about poor James Francis Bate. If he's the James Francis Bate who was William John Bate's son, he was born in 1836 so was only fourteen in 1850 ... I can't find that he married, or when he died; in the 1861 and 1871 census data he is single, and an agricultural labourer.