Liquid Solution:
For really stubborn lead removal try a 50/50 mix of 3% Hydrogen Peroxide (the common drug store variety) and white vinegar. Plug the bore, fill it up using a dropper or syringe and let it stand for 2 to 3 minutes. (Do not let it stand for too long.) You may get some foaming so protect the barrel's external finish, as this solution is not kind to bluing. Drain and wipe out the black muck that used to be lead and then immediately clean well with bore cleaner.
Note:
While most people have used this solution without a problem there have been reports of this solution pitting some mild steel barrels. The factors involved in this seem to be the type of steel, the presence of rust in the barrel, and excessively long soak times leading to chemical changes in the solution. I strongly recommend not letting this solution soak more than 2 to 3 minutes.
Do not exceed the 2-3 minute rule, it can ruin a barrel if left for hours. You can repeat as needed, basically when it stops bubbling it's done.