My first thought on seeing the name Levis and Rachel and Reuben was to look for Jewish registers, but I can see that all the registrations of major life events were in Church. With the dates involved that will mean searching through parish registers, which are probably not indexed. I'll take a look though.
I've found many old testament names for Levis children, but assumed this was in fashion back in the 18th and early 19th century (as well as their re-cycling of the same names over and over again).
Similarly, I've found many records for Levises with the CoE, various types of Methodist, Baptist, Quakers and other types of protestant dissenters, but for the Leicester/Lincolnshire Levises I have not ever found any Jewish (or Catholic) entries.
I've found Catholic Levises that came over from Ireland, and a few Jewish ones in London (1870-1890 immigration wave from the pale of settlement), but nothing that indicates these are related to the Levises that were already living in England in the 18th and 19th century.
There is a relatively sizable contingent of American Levises that descent from a Samuel Levis who emigrated 1680-ish to Pennsylvania (and these were quakers). Some of these descendants make the claim that they are related to the French 'de Levis' aristocratic family.
I match these American male-line Levis descendants through Y-DNA testing, even though I cannot trace back my own lineage to connect to their ancestors (my direct line has never emigrated to north American as far as I am aware). The Y-DNA haplogroup for these Levises is downstream of I-M253, which is not a Jewish haplogroup.
My personal estimation is that the name 'Levis' is more likely to come from a Danish farmer named 'Leif' or 'Leiv' than Jewish or aristocrat French ancestors.
Of course this doesn't relate directly to the Stanion Levises (until we can prove or disprove their link), but the name Levis is rare enough for me to believe they are very likely to be all related to each other.
