I just found a Civil War records site, http://www.censusdiggins.com/nc-civil-war-har.htm
and it has information on 2 of Adlai's older brothers. It looks like Samuel had 3 sons fighting in the Civil War:

HARDIN, John J. Co B, 2nd NC Cavalry Enlisted 6-18-61 at Iredell Co, NC. Private, age 26. POW 7-28-62 in NC. Exchanged 10-6-62 at Aiken's Landing, NC. POW 9-10-64 near Petersburg, VA. Imprisoned at Point Lookout Prison, MD where he died of pneumonia on 2-19-65.

HARDIN, Leander Co A, 4th NC Infantry Enlisted 6-5-61 at Brunswick Co, NC. Private, age 22, resides Iredell Co, NC. POW 9-22-64 at Fisher's Hill, VA. Held at Harper's Ferry, WV. Transferred 10-1-64 to Point Lookout Prison, MD. Exchanged 3-29-65 at Boulware's Wharf, VA.

Hey Lee, I always thought that Lee was a nickhame for Adlai, because my dad often went by the name Lee. But it looks like it was also the nickname for Leander, as that was what the above was called in 1850 but then he was called Lee in 1860.