Need a better look to see if there is a fly in that lock. Pull the hammer to full cock. Holding the hammer to control the fall, lift the sear to release the hammer from full cock. as the hammer rotates slightly out of the full cock notch the nose of the sear should ride along the tumbler. The nose of the sear should follow the tumbler past the half cock notch as the fly will lift the sear over the half cock notch. The tumbler then will rotate to the full down position. If the sear does not stop during this slow release, you have a fly.
It's time to put some marking agent (lipstick? candle soot?) on the tip of the sear lever and install the lock back in the mortise. Work the lock and after removal, look for markings in the lock mortise where the tip of the sear may be rubbing. If there is a mark, then some wood may have to be removed, or the sear arm needs to be shortened.
The trigger will have to be removed from the stock to see if the strong spring that drives the release lever needs to be tightened.
From the original description, the sear is not being struck hard enough to lift the nose of the sear out of the full cock notch. Either the sear lever is dragging on wood inside the lock mortise, or the sear is not being struck hard enough by the release lever in the trigger.