Pedersoli intentionally installs a set trigger screw that is too short in the location that adjusts how much the front trigger engages with the cocked rear trigger. This is the screw that is located between the two triggers.
I think they do this to prevent the user (you) from being able to adjust the triggers into a dangerous condition.
The only way to get the screw to do its job is to install a longer screw. One that actually reaches the "catch" area of the front trigger.
This screw does not adjust the power needed to get the front trigger to release the rear trigger and make the gun fire. It only controls the distance the front trigger needs to be pulled to release the rear trigger.
Some of the other factory guns on the market do come with a screw that works like it should and I know of two cases where the gun owner misadjusted that screw.
The owners came to me saying, "My set trigger is broken. It doesn't work."
Looking at the gun and trying to set the rear trigger I found that they were right. The rear trigger wouldn't stay "set".
In no time, using a small screw driver to unscrew the adjustment screw I had it fixed and working like it should.
The right way to adjust the screw (assuming one with the right threads and length can be found) is to unscrew the little screw so that it is almost out of the trigger plate. Then, set the rear trigger.
Screw the screw back in slowly until the rear trigger releases. (Keep your fingers out of the way. That rear trigger snaps forward with a LOT of power.)
When the trigger releases, unscrew the little screw 1/2 to 1 full turn. Then, check the trigger by recocking the rear trigger. It should latch into place if it is pulled far enough back.
Speaking of that rear trigger, for reasons unknown to me, the spring for the set (rear) trigger on Lyman guns is way stronger than it needs to be so expect to use a LOT of force to get it far enough back to let the front trigger "catch" it and hold it in place.