Hi Jethro
First question .There is a marriage of a Jane Nash at St george Hannover Square that fits.
John Youmans bach of this parish and Jane Nash spinster of this parish by banns 5th Decemver 1768.
Witnesses John Barrows and Ann Robinson
But I can't find a burial for him or Jane.There are tons that could be him.I assume he must have died beteen 1768 and the childrens births.
Secondly there is a Joan Sandham baptised at Petworth 3.1.1671 d of Henry.
This might explain why there were only 3 children as she would be 38 when Sarah was born.
There is a brother Henry 13.5.1677.The others are older Elizabeth 8.2.1662,Henry 12.8.1664,Will 17.9.1765.
Henry married Sarah Arnall at Petworth 23.4.1662.
There are several possible deaths and baptisms for him.
Bapt 10.12.1639 to Henry and Mary or 8.8.1630 to William Sandham.
Back to the Lutmans
John's children -Elizabeth 4.1.1671,William burried 30.12.1676,Peter 29.6.1676,Charles 18.1.1678-16.2.1680 ,and a very late Mary 7.8.1794
A couple of possible deaths but no marriage that fit the bill in Sussex
John bapt 10.1.1647 s of Thomas Lutman
Siblings -Margaret 28.6.1641 and Jane 18.12.1644
Again short of a marriage and more than one possible death for Thomas Lutman
Thomas bapt 18.6.1620 s of John Lutman
Siblings Jane 1.9.1616
Marriage John and Margaret May at Petworth 14.2.1608
Burial Thomas 8.9.1670
Then we have Wills which may add some light on the family and an inhertitance distpute.
Thomas Luttman vs Vousden 1681 National Archives reference C5/519/93 Petworth
John 1642 of Petworth at Chichester .
Burials John 1690 no date given,John 1699,,Richard 19.3.1736,Mrs Alice Lutman 27.8.1742.(Could possibly be John's wife)
That's all I can see for now
Ciderdrinker