If this is the same guy I'm thinkinf of then, yes, he's a bit of a bugger to pin down. He doesn;t seem to appear in the census records too often and even then its down to interpretation. Through my own research into my family history combined with assistance form others, I have come across Joeseph as my great-grandfathers brother.
Elizabeth was from Greasley (Sometimes appearing in records as being from Brinsley the neighbouring village). But George was a Yorkshire man and after their marriage they seem to have moved to George's home town of Pontefract in Yorkshire where their children were born.
So searching Brinsley (Joseph's mother's birth place) you are unlikely to find the correct information. Try looking for him in pontefract.
Another thing to point out is the surname. Try looking for LUND instead of LUNN. At some point during the start of the 19th century the name changed from Lunn to Lund.
I assume we are looking at the same eprson here, as all the other information you rpesent ties in correctly with the research I have. Joseph had several brothers and sisters, 6 I've found so far.
I can get certain ammounts of info from Ancestry but living names aren;t there. As soon as we get past Josephs grand children we just get "Living Lund" instead of a name. There is a Pauline Lund who died in 2007, don;t know if you are aquainted with her, but she appears to be the last Lund on that side to appear as a full name and age.
Hope this helps. PM me if you want more. Incidently, have you managed to get any further back than William and Isabella Lund (George's parents)? I have a possible John Lunn but no certainty and after getting back to William and Isabella the trail goes blank.