I have found this family in Carlisle 1851,. Is it yours?
HO107/2429/309/54
Botchergate, Carlisle
William Lennox, head, 42, Labourer, born Scotland
Ann, wife, 38, labourer, Scotland
Juna, dau, 14, Scotland ( this looks like Jane to me, wrongly transcribed by Ancestry)
robert, son, 9, Scotland
Elizabeth, dau, 6, Carlisle
William, son, 5, Carlisle
Mary, dau, 3, Carlisle
Ann, dau, 1, Carlisle
If it is yours, I'll check 1841, Scotland to see where they were then.
Jen