Darn, I was hoping for a Whitworth, but it is not.
It is a pretty standard 19th century US muzzleloading hunting rifle, plenty for squirrel and other small game, adequate for deer if you are a good shot and a good hunter. It was built in a small shop by whoever L&K were using a lock made by the Manton family in England and imported to Pennsylvania or Kentucky. Lockmaking was precision work in those days and it was a lot easier to buy them from a maker who was set up for fine work. Larry & Kurly may have bought a factory made barrel, too; and just made the stock and installed the works. The day of one man making everything on the gun was likely gone by the time this rifle was built.
The two triggers are a "double set trigger" installation. When the gun was in good condition, you fired it by cocking the hammer, and pulling the rear trigger until it clicked into engagement. Then a very light pull on the front trigger - measured in ounces on the good ones - would actually fire the shot. The screw between the triggers is to adjust the pull from a few ounces to a few more. It may be worn or rusted and no longer work right.
Maybe somebody will recognize who trademarked their guns L&K but bear in mind that there were a lot of small operations and they did not keep good records in those days.