He probably died between 1915 and 1920 in Iowa, although it is possible that he moved elsewhere after 1915.

Be careful not to confuse him with James L. Goodman, born 18 Dec 1840 in Indiana, who died 28 Mar 1925 in Carter Co., Ky. That James Goodman was recorded in Carter Co. in both the 1910 and 1920 censuses, with a wife Margaret (nee Hall), and birthplaces given as Ind Ind Ind, while this James Goodman was recorded in Iowa in 1910 and 1915.

I cannot find this family in the 1870 census. They may have been in the process of moving to Elliott county from Rowan or Morgan, and been thereby missed. (Since it usually took about three months in those days for the census to be completed, families were easily missed if the new location was visited before the old one.)

1880 census of Elliott Co., Ky, enumerated 18 June, lists on p. 30 as family #196:
Goodman, James, 39, farmer, b. Ky Va Ky; Rachel, 39, wife, b. Va Va Va; Ida F., 12, dau; John M., 10, son; William L., 8, son; Henry F., 6, son; Maranda R., 4, dau; Edmund R., 4, son; Lucindy B., 10/12, dau. All children born Ky Ky Va.

1900 census of Elliott Co., Ky, Brown precinct, enumerated 19 June, lists on p. 15B as family #248/254:
Goodman, James, 59, b. Dec 1840, Ky Tenn Ky, farmer; Rachel, wife, 59, b. Sep 1840, Va Va Va, married 33 years, mother of 9 children, 7 living; Miranda, dau, 24, b. June 1876; Lucinda B., dau, 20, b. July 1879; James M., son, 19, b. Mar 1881; Lewis C., son, 15, b. July 1884. All children born Ky Ky Va.

1910 census of Buena Vista Co., Iowa, Scott township, enumerated 21 April, lists on p 3A as family #44/46:
Goodman, James, 70, b. Ky Va Ky, farmer; Rachel, wife, 70, b. Va Va Va, first marriage for both, married 42 years, mother of 9 children, 7 living; Belle, dau, 27, single; Mifford, son, 26, single, farm laborer on home farm; Louis C., son, 23, single, farm laborer on home farm. All children born Ky Ky Va.

The 1915 Iowa state census cards record the following members of this family, all living in Sioux Rapids, Buena Vista Co:

James Goodman, 75, married, retired, b. Floyd Co., Ky, father b. Tenn, mother b. Ky
church affiliation none, residency 8 yrs
Rachael Goodman, 75, married, b. Scott Co., Virginia, both parents born in Virgina
church affliiation blank, residency 8 yrs
Lucinda Belle Goodman, 34, single, b. Elliott Co., Ky, father b. Ky, mother b. Va
church affliiation blank, residency 8 yrs
James Milford Goodman, 33, married, farming, b. Elliott Co., Ky, father b. Ky, mother b. Va
church affliiation blank, residency 8 yrs
Lewis Cleveland Goodman, 29, married, farmer, b. Leadingham, Ky, born parents born Ky
church affiliation Baptist, residency 11 yrs
Mary Jane Goodman, 20, married, b. Leadingham, Ky, born parents born Ky
church affiliation Methodist, residency 11 yrs
Mildred Goodman, 4 mo, b. Sioux Rapids, Ia, borth parents born Leadingham, Ky

These cards are in alphabetical order by name across a whole county, with no cross referencing, so other records are required to create family groups. Mary Jane is Lewis Cleveland’s wife, and Mildred is their daughter. Although James Milford was married, there is no card for his wife. She was probably back in Kentucky.