Copper is slightly soluble in lead and readily soluble in tin. The idea of tinning the copper is to put it in contact with the melt. Without tinning, it is insulated by a layer of oxide. So, once tinned, it will dissolve up and until saturation point at the temperature of the melt.
There was a guy who went by antimonyman who sold a powdered flux that made it easier to alloy antimony into lead alloys, I am sure the flux would help copper dissolve into the melt too.