I hope this doesn't confuse! 1841 census John SWIGART 1791 (should be lingard) with children, ellen, john, william, alice and thomas (1832/6) and 1881, the son William (57) is a rush manufacturer the same as his late father John. John's wife must have died before 1841 as she does not appear on any census.
The other branch is John Lingard 1803 marries Mary Wilkinson 1851 census which you rightly have from Greenhalgh.
On the 3 marriage certs for son Thomas Lingard it does state that his father John is deceased, but to tie this up a baptism or birth , or mother's name would help!