I would take the lock apart. It is easy, just remove the two screws on the opposite side of the lock.
You can watch the bridle as it cocks. The first notch or catch will be the problem. It can be filed deeper, but you are better off contacting Lodgewood.com. They will have the spare part. If you remove the mainspring, take care. I use visegrip pliers. There is a special tool for removing the spring. Lodgewood has these. I have noticed this is a common problem with muskets.
If you pull the trigger hard enough, most of them will release the the hammer. I have an almost fine P-53 Enfield that does not catch on the half-cock.