The best place to order parts for a Lyman lock is from the Lyman website.
From your description I don't fully understand what your hammer is doing. But seeing as I have tuned those locks and triggers I have can give a pretty good guess as to your problem.
The lightness of your set trigger pull will have nothing to do with it. The Lyman set trigger is a double bar trigger, meaning it can be fired set or unset. When set, it releases a spring loaded "striker" that "snaps" agains the sear. It has no real power behind it. Except for the back spring in the trigger which on a lyman is strong.
You can get this rifle to fire by pulling the trigger in its unset mode. This works because you have leverage and pull until it releases the sear.
This indicates to me, that your wood has swelled in the lock mortice area and is putting pressure on the sear.
Smear some lipstick on the sear and bridal and put the lock back in the gun, tightening down the lock screw as normal. Take it back out. You will probably see lipstick on the wood from where both the sear and bridal screws are touching. Get a small sharp chisel and carefully remove this wood until it no longer touches.
When you get your lock back to normal try it again and it should work.
Leave the fly alone. It's purpose is to allow the sear to override the halfcock notch when you actually fire the gun.
If you have dissasembled the lock you may have galled up the sear screw, this will cause friction. If so either polish it back smooth or replace it.
After all is working well again, seal all endgrains with sealer or tru oil. Better yet, redo the entire stock.
At the least, remove butt plate and toe, trigger guard and plate, breech and lock from the stock. Now put a couple of good coats of regular Johnsons Wax on everything. You especially want the exposed endgrains in the mortices to be covered.
