Broken drill bit.
Old topic I know.. But I just did the same thing, broke a drill bit deep inside a lead part.
Turns out it was an easy fix - I exposed part of the broken drill bit by digging around the 'stump' using a small flat blade screwdriver, then I heated the broken part up using a small but sharp butane flame. The drill bit heated up and slid out of the lead using a pair of tweezers. It was then it was as easy as feeding a stick of lead through the butane flame into the pre-heated damaged hole, a quick file, and re-drilled as normal.
Hopefully this could be useful to someone else in the future - I never realised how grabby lead can be on a drill bit!!