The compensating screw in the action knuckle is meant to put the gun back on face... period. Many people try to move this screw for the wrong reasons, and many people bugger it up in the process.
If the top lever has moved left of center, it is not really a problem unless the bolting is loose. A Syracuse Lefever is only bolted by a single top bolt which engages the rib extension. It is wear in the bolt or the notch in the rib extension (or both) which allows the top lever to gradually move left of center. If it becomes necessary to tighten the bolting or desirable to bring the top lever back right of center, the best way is to make a new bolt that is a few thousandths thicker than the original. The bolt has a slight taper, and it needs to be fitted, polished, and hardened, but it isn't a very difficult or complicated job. Occasionally you will see a gun that some jackass attempted to tighten by hammering on the rib extension in an attempt to slightly close the notch. This is crude blacksmithing, not gunsmithing.
The earlier Lefever guns had a screw on top of the action to tighten up the bolting, but this compensating feature was eliminated as the design evolved. If you look at the pivot lever E grade currently listed in Gunbroker item # 781458036, you can see this compensating screw in photo # 9 between the doll's head rib extension and the pivot lever.