There's an outside chance that his pension papers might shed light on his Masonic association, see:

Luther M. Sabin, Major 44th Illinois Infantry, filed pension Application No. 1199157, February 2, 1892, Certificate No. 786684 [Numbers not that clear on-line], died March 2, 1903 at Soldier's Home, ??

NARA T289: Organization Index to Pension Files of Veterans Who Served Between 1861 and 1900