As you probably know, the IGI has Willingham by Stow baptisms ... but no Hannah. It has the following Lambert/Lamberd/Lambard baptisms, all children of William (no mother named).
Rebekah 1794
John 1796
Mary 1798
Elizabeth 1801
William LAMBERT was buried at Willingham 17 Nov 1834 age 83
a Mary LAMBERT was buried there 16 April 1834 age 80
also an Elizabeth age 25 on 12 March 1827.
A William LAMBERT married Mary ELSOM at Corringham (5 miles to the north) 16 Aug 1774, where they had
John 1774
William 1777
Richard 1780
A mile south of Corringham is Springthorpe, where they appear to have had
John 1780
Sarah 1782
Joseph 1785
Ann 1787
Benjamin 1789
Mary 1792
Two things to note
1) If they are all children of the same couple, Mary would have been getting on a bit by the time the last child was born ... I think it's juuuuuust OK.
2) The baptisms of Richard and John in 1780 in different places just two weeks apart. My first thought was that a year had been wrongly transcribed (a year out) but as both the given dates were Sundays, this was probably not the case.
This last fact apart, the marriage and three sets of baptisms form a coherent pattern, as do the burials.
If Ann 1787 was Hannah (BAINES), the presence of Charlotte 1836 would seem to push Hannah's childbearing years to the limit.