Jackson C. Lovejoy was a resident of Tallahatchie County in the 1860 Census and enlisted in neighboring Yalobusha County.
He and apparently several of his brothers are all listed in the roster of Company D, Fishing Creek Avengers (raised in Yalobusha County), 29th. Mississippi Regiment Infantry.
Jack Taylor provides a regiment history and roster list at this site.
http://www.geocities.com/jack_taylor2/
Also see this site.
http://mississippiscv.org/MS_Units/29th_MS_INF.htm
Individual service records can be ordered by clicking on the banner at the top of this page.