I don't know when Narragansett Armes went out of business, but they built (or at least intended to build) a very interesting variety of historical guns and rifles. I have their catalog from 1999, with the year 2000 update inserted. The catalog shows full-length, lock-side views of their various offerings, with pretty good descriptions. The descriptions identify the type of lock which was used on each type of firearm.
A few of the guns, like their Brown Bess, the Spanish Catalan musket, and the English snaphaunce musket, used special custom locks, but most of them used regular commercial locks from Chambers, L&R, or Siler. However, I believe their guns were built to order, and some options may have been offered. From the two photos provided in the original post, I can't tell for certain which model of rifle you have. I see the double-set triggers, and that appears to be an iron or steel triggerguard. Knowing the model of rifle may help with identifying which lock was used. One page of the Narragansett catalog was devoted to showing the locks used on their firearms:
However, even with these images right in front of me, I can't tell for certain which lock you have. That wide, flat-faced cock or hammer screw looks like the one used on Siler locks, but the shape of the lockplate is markedly different from the Siler, and the rounded pan and the frizzen screw with the external head suggest the lock is not a Siler at all, or an L&R Classic. It actually looks a lot like the
L&R RPL-06-F lock with ornamental grooves added on the tail. I'm not saying that's what it is, but it kind of looks like it.
Regardless of the maker of the lock, your best bet may be to send it to Brad and Shane Emig of Cabin Creek Muzzleloading. Brad advertises in
MUZZLELOADER magazine as "the Lock Doctor," and he really is a master of the craft. I'll bet he could get it fixed right up for you.
Good luck with this!
Notchy Bob