How can I attach a copper puipe to an existing lead pipe?

You can by an adaptor called a 'lead-lock'.
You may need to shave the lead a little to make it fit, be careful not to overdo it.
Tighten up, don't damage the lead when you do...always use grips and spanner to restrain the fitting when tightening.
Copper fits in other side...again restrain the fitting when tightening up.

Nige
December 2009

Hi
You need to go to a Plumbing Merchants and ask for a Copper to Lead compression connector and you will be able to join them together.

tyemanone
December 2009