You may know all of this but I'll go thru it anyway for those who don't.
The lock has an arm that sticks out away from the lockplate at about 90 degrees. This is part of the sear that holds the lock at half or full ****. If it is moved upwards while the lock is cocked, the tumbler and hammer are released.
The front set trigger has a blade on top of it that rests right below the sear arm. Pulling the front trigger moves its blade up against the sear and pushes it further upward releasing the lock.
The front trigger also has a catch on it that holds the rear trigger in a cocked position.
The rear set trigger is just a spring loaded device with a blade on top of it like the front trigger.
When it is 'cocked' a spring is trying to push it upward but the catch on the front trigger has engaged its catch and is holding it in the cocked position.
Once set, when the front trigger is pulled, it releases the spring loaded rear trigger which slams forwards driving its blade into the sear arm. This should be enough to cause the sear to release the full **** notch causing the gun to fire.
Several things can keep this from happening.
If the rear triggers spring has been adjusted to reduce spring pressure, there might not be enough velocity given to the rear triggers blade to knock the sear out of the full **** notch.
The blade on the rear trigger might be hitting a small piece of wood as it flys upward. This can reduce or even prevent the rear triggers ability to hit the sear arm with enough force to release it.
The sear arm might be hitting the stocks wood making it hard to move.
In this case, this is unlikely because if the sear arm hits the wood, it usually won't allow the lock to be cocked.
Remove the lock and the set trigger and look for things that would keep the parts from moving as I've described above.
Have fun.