The 1860 census shows child named Levi Easley, age 2, on the census of 1860.

Assuming that's not who you have in mind, a man named Levi Easley and his family came to Alcorn County MS before the 1870 census. In 1860 Levi and Polly Easley lived in Obion County TN.
A service file exists for L. D. Easley in Co. "K", 33rd Tennessee Regiment. This company was recruited in Obion County TN.

One further note -- on the 1870 census for Alcorn County MS, children of this couple are listed as having been born in Missouri in 1862 and 1864.