For most doubles, the lever is moved to the right to open the gun, and it returns back left toward center when it is closed. As the bolting surfaces wear, the lever then gradually moves further left, and eventually may move left of center.
The point where it stops can also vary somewhat due to how easily or sharply the gun is closed. And a weak top lever return spring can also affect where it stops. For the end of the top lever to stop a full inch right of center, as you mentioned, seems awfully extreme, and could indicate that someone peened or welded the bolting surfaces to make the gun appear not worn.
Some earlier Syracuse Lefever shotguns, referred to as "pivot lever" guns, have a different bolting system, and the top lever always returns to center. These guns had a compensating screw to take up wear and keep the bolting tight. Later models simply self-adjust by the process of the lever gradually moving further towards the left as wear occurs.