There are researchers on this forum who are much better, but my search of Robert Lemuel Montgomery in FOLD3 and Ancestry found no CW records. As you know in 1860, R. L. was 40 years old with 4 kids and was a blacksmith. More than likely he did not enlist when the war began, but would have been eligible under the 1862 conscription act. Being a blacksmith might have kept him out of the army if he was able to apply his skill in a manner that made him more valuable at his trade than in the ranks. Just a thought. Good luck on your search.