The making of shot would have been a military trade. Those using shot in civilian life, such as gamekeepers and huntsmen casting their own.
However the forces during the civil war would have required vast supplies of ammunition. Musket balls would have been made from lead, which would have been melted down and cast in moulds to create shot.
Generally the shot would have been mass made, and would not have been an accurate fit for the individual musket. Incidentally model shot gun bores are based on the principal of the number of lead musket ball that can be made to a pound of lead. hence 12, 16 and 20 bore.
As for the source of lead, typically this would have been looted from the nearest source. church roofs often gave generously!