An 1816 Large Cent With Specific History Attached To It .

My thought is both, perhaps. I've seen many c/s's that were punched on the bias, so to speak. This effect results in the stamp being more prominent and conspicuously not part of the design. Also, note that this stamp is large, compared to many. Oftentimes, those applying small stamps tended to more carefully place them in a field or else incorporate/align the mark with the coin's design; this, a more artful approach, if you will.

Lysander's history tells us that he was a social sort of guy, As a mason and/or lodge member, he might well have pulled this coin from a pocket, like a calling card, as a means of introduction with a stranger. He could the follow-up with, "I apply this name stamp to rifles I make." Personally stamped coins were typically carried by masons and odd-fellows back then.

Another aspect to consider is that these were the old days, prior to folks carrying credit cards and driving licenses. During the Civil War, many soldiers carried a stamped medal, bearing their name, rank, regiment, etc. These would help identify their remains, if need be. More commonly though, a soldier's name was applied to his clothing. Identification was even somewhat important back then.

As an aside, these Civil War identification medals, typically made by diesinkers and stamped by sutlers, currently fetch between $1,500 and $3,000, apiece.