A picture would be handy here.
Sometimes, lead pipe will go into a cast iron hub fitting.
Lead is gray though.
If it's a black pipe, is it plastic or cast?
If it's one of those, then a coupling should work on it.
If it's gray lead, then most of the time, 99% and I want to extend or replace, I pull the lead from the hub, use a rubber fernco hub seal and insert a new pipe into the hub.
Some plumbers will pour a new lead joint.