Hi Michael

James was buried Maughold, Frances would be able to suggest which cemeteries that might be.

Looked again on LDS IGI Family History site to find Mary's death , appears there are no Death records on line for Illinois prior to 1877 which is strange, I am sure they must have been recording deaths before that.

Looked at Find A Grave Illinois but became confused seems showing Lynn and Galva in County of Henry not Knox.

Looked for Mary any name in:

Galva Cemetery , 6500 internments , 84% photographed.

Galva East Cemetery 990 Internments, 71% Photographed

St Johns Cemetery Galva

Swedond Lutheran Cemetery Lynn Center

Did not get a match. As an Aussie I have no idea where these cemeteries are in relation to Lynn. But I think you should check all close ones, in those days they did not travel far to bury the dead.

Looked back at the hand written Census, and Margaret was 9 months - could not find her birth. Relationships not shown on US Census, but assume she was dau of James and Judy/Julia. And appears she died soon after as new Margaret appears in 1870 below. Also next door in 1860 - same census page:

Lynn Township, County of Knox
, Post Office Galva

John Corlett 55
John Corlett jnr 21
Thomas Corlett 18
David Corlett 17
Robert Corlett 16
James Corlett 15
Mary(?) Kelly 15
???? Corkhill 6

All born IOM , and next to them

Thomas Kelly 32 b IOM
Marian(?)Kelly 30 b IOM

1870 US Census Lynn Township, Knox County.

James Kirmen 48
Julia Kirmen 37
Jane Kirmen 9
Margaret Kirmen 6
Robert Kirmen 4
John J Kirmen 2
John Carlett 65
Daniel Kinsdale 78
Mary Kelly 23
William Carlett 17

All born IOM Except James & Julia's children born Illinois

David