Isn't the hook adjustable on the Lefever ?
Actually, they have an adjustable ball socket that takes the place of a hinge pin. Early Lefevers had several wear compensating features, but most were dropped over time as they proved to be both unnecessary and costly. As Miller noted, there are several different cocking systems, and the correct barrels of the correct type must be found. Then, with the cocking hook models, it is sometimes found that any but very minor addjustment of the ball socket will push the barrels back enough that the pin in the lump that engages the cocking hook will now slip past it without cocking the gun. This is also assuming that one can even turn this adjustment screw. Many almost seem as though they were set with some 19th century version of Red Loctite, and defy efforts to turn them. We also see quite a few that have been buggered by attempts to move them.
Jim, if you have barrels that actually are within .001" of closing, they very possibly could be fit to that gun by the smoke and stone method or backing off the adjustment a small bit or some combination of these. But if you do stone, or otherwise remove metal, they may then be loose on the parent gun and really hurt the value.