As for 4th Reg't, Mississippi Cavalry is concerned, there are no filings for any LEEs
As for Nancy Harriel LEE, there are no filings for N. LEE, Nancy LEE, Nancy H. LEE, or N. H. LEE
As for Elijah LEE, There is a 1914 filing by Mary LEE, in the name of her husband, Eli LEE, 7th Mississippi, in Pearl County. There are no filings under the name Elijah LEE.
Not much to hang your hat on, I am afraid.
Dennis