John E is correct on the purpose of the screw. These early Lefevers prior to around 1890 used a vertical bolt which entered the slot in the Doll's Head from the rear. That screw protruded down through the top tang & bore against the top of the bolt. Thus if the gun did not bolt up tightly turning that screw down took care of it.
To the best of my knowledge, all the rod cocking hammerless guns used this system whether they were thumb push or pivot lever. Beginning with the Two-Hook guns the bolt became an extension of the top lever & was wedge-shaped, swinging into the notch from the side & was self-compensating.
It likely also has two small screws in the bottom of the frame. These turn in as a stop for the lower leg of the mainspring. Although Lefever referred to them as having rebounding locks they were not "Truly" rebounding. Once the expansion of the V mainspring was halted the hammers were simply free floating. They had ample inertia to fire the gun but then were not Locked into the primer indent so there was little or no firing pin drag on opening the gun.
Later guns did not have this adjustment but all of mine seem to have been Factory Set so that with the hammers down the firing pin tip is about flush with the breech face.
What's Not to like about a Lefever
