Hi Bowjo. Welcome to the Forum.
The screw between the triggers adjusts the engagement of the front triggers latch with the rear triggers catch.
Think of a small flat surface sticking out from the rear of the front trigger. The rear trigger has a small shelf that moves down as the rear trigger is pulled to set it.
When the rear triggers shelf moves below the spring loaded front triggers flat, the front trigger moves slightly forward as its flat slides onto the rear triggers shelf.
This screw limits how far the front triggers flat overlaps the rear triggers shelf.
It DOES NOT ADJUST THE FORCE NEEDED TO PULL THE FRONT TRIGGER. It only adjusts the distance the front trigger needs to move to release the rear trigger.
For safety reasons you want the front trigger to have to move a little bit to release the rear trigger.
The screw behind the rear trigger adjusts the force of the heavy spring that drives the rear triggers blade up against the locks sear arm.
If the set trigger is reliable releasing the lock from a full cock position, don't mess with it.
To adjust the front trigger using the screw between the triggers follow these instructions:
1. Place the cock or hammer in the fired position.
2. Back out the small screw between the triggers at least 3 full turns.
3. Cock or "set" the rear trigger listening for the distinctive "click"
4. Slowly screw the adjustment screw in until the rear trigger is released.**
5. When the rear trigger releases, back off the adjustment screw at least 1 full turn.
Your done.
** The Lyman Great Plains Rifle (or Hunter) is intentionally supplied with a trigger adjustment screw that is too short. The screw cannot release the rear trigger even though it is screwed in all the way.
Note: With the hammer or cock resting in the fully fired position you can set and release (snap) the set triggers all day long and not damage anything.
If the hammer or cock is at "half cock" and you snap the set rear trigger you can bust the half cock notch in the locks tumbler or break the nose off of the sear. Either of these things will require that you have the lock repaired.
Do NOT "fire" the set triggers if the gun is at "half cock".