Hi Nick,
From what i have found Joseph died before the census began, but with so many Jospeh Brooks's in Lincolnshire its nr impossible to determind a date. The elizabeth he married was of maiden name Barker, born abt 1784 in Tattershall. She is in the 1841 Census in Tattershall living with two children Ann and John, here she is described as a widow. In the 1851 Census, Tattershall she is housekeeper to her son Charles who is a Master Tailor, and she is still with him in the 1861 census. She died in 1867. I am happy to send you the census images if that is any help to you and your friend.
All the best,
Angela