3rd Model Winders, the most common type, had the Lyman sights.
On earlier models, the barrels were drilled & tapped for the standard US military sights of the day.
Damage to the windage adjustment parts on the Lyman sights for the Winder is pretty common. If the rifle was knocked over, the rear sight took much of the impact. Depending on how the rifle landed and how high the elevation was set, damage can be extreme.
Often, the two arms that extend over the top of the action can be straightened, but sometimes they break off. The smaller windage adjustment moving parts were not unique to that particular model of Lyman sight. Parts salvaged from other sights may well fit.
Those Winder Musket actions were frequently used as the basis for a custom rifle back in the 30s-40s-50s. The Lyman sights, not things of beauty, were usually discarded. They can be found in the spare parts boxes of gun shops of the day.