I slather some gel or foam (either works much more effective than runny liquid) in there and then forget about it until the next day.
At that point the lead and crud should be greatly softened up, if not outright liquified, and you should just have to push two or three patches through to get it literally squeaky clean.
If it was abominably dirty, you might have to give it a quick hit with a bore brush before the patches, but whatever the case its best to give the chemicals enough time to do the real work for you.