This is pretty standard. First, do not use anything in the way of lapping, abrasive to do this, as you're likely going to hurt the bore.
Use something purpose built. Get some IOSSO bore cleaner and preferably a couple of their hard nylon brushes. This stuff is purpose built for lead/carbon. You need to brush, patch it several times, you have layers of both lead and carbon. The patches will be charcoal black and get progressively lighter. After a few cycles, use a patch wrapped tight around the brush, soaked up good with the cleaner and you will get to bare metal in short order without hurting anything.