Is the Lefever a side lock or side plate action?
The later Lefevers were an innovative boxlock design with false sideplates. Earlier models were somewhat of a hybrid, having sears mounted on the sideplates. Some grades have sear engagement adjustment screws on the sideplates. Hammerless guns had several different cocking systems including side lever cocking, rod cocking, two hook, small single hook, and finally the large cocking hook. There are several different bolting systems. Then there are numerous little variations in the design and internal parts because Dan Lefever was always trying to refine things. They are not cookie cutter guns like many American doubles.
So a good Lefever gunsmith is one who is familiar with all of these variations. The design is fairly simple and easy to diagnose if you have knowledge and experience. But time is money when you have a gunsmith unfamiliar with Lefevers. Messing with the vaunted compensating screw in the knuckle can open a whole new can of worms. Guys like Buck Hamlin and Keith Kearcher, who worked on them a lot, also seemed to have a good inventory of spare parts from the different eras. It's a lot easier and cheaper to simply replace a worn or broken part than to machine onefrom scratch, so they had an advantage in that respect. I have heard good things aboout Jerry Andrews in Moundsville, WV. I bought a couple Syracuse Lefevers from him, but I do my own repairs, so have no personal experience with his skills fixing Lefevers. He is said to be good with L.C Smith's too.