You want to replace old lead pipe connected to cast iron sewer pipe with copper How do you connect the copper pipe to the old lead pipe or to the cast iron pipe?

When I have to connect copper to lead "D" I usually solder the copper to the lead or wipe a lead joint depending on the diameter

To connect copper to cast iron ,.... If there is a hub I caulk the copper directly into the CI with oakum and poured lead (molten) OR one can solder / braze a female adapter fitting and screw the copper into a CI female fitting