Thanks to both of you.....yes, I think who William was (or who the Williams were) is the key here., although it's Lyon & Betsy who are (or should be....because the William issue is very interesting too) my main focus. For some time, I've discounted the William in Arnold as being from a different Asher family, but, as jim said, it could simply be that he decided to move out of the city centre & thus became a labourer.
When I first started looking at this, I assumed that Lyon & the William who had the son Samuel Lyon (ie the one we know was a hawker in the city centre....whether he later moved to Arnold or not) were brothers.....can't be sure of that....maybe William was a nephew or a cousin or a distant relative of some kind. What would be interesting about that would be that, IF they were brothers, IF this William was the one in Arnold with Elizabeth & IF the census is correct that William was born in Nottingham & not in Germany, then it would mean that Lyon's parents also came to Britain.
To complicate matters further (aaaarrrghj !) there was a Joseph Asher living cheek by jowl with Lyon & William in Nottingham city centre. At first I'd assumed that he, Lyon, & William were brothers, but Joseph was born in approx 1780 in Packington, Leicestershire. He seems to have been much more firmly established &, obviously, his parents were in Britain when he was born.....I don't know if they were part of the same family that came over earlier, a separate East European rooted/Jewish Asher family, or a "native British" Asher family. Today, I've had a message from someone who's researching Joseph & his line, so I might be able to piece something together with them.
Thanks to both of you very much