This is all incorrect. If steel is quench hardened (case hardened) it does have a surface hardness but lead is not steel and does not respond like steel. Lead will be the same hardness all the way through. It's possible that the middle may take a day or two longer to reach the final hardness because it cooled last but it will be the same all the way through as long as it contains antimony (Sb).
That is the metallurgy of lead. You cannot "case harden" lead. Heat treated either by quenching from the mold or oven heating and quenching will be the same hardness all the way through. It is possible to work soften the outer edge of the boolit a bit by sizing which is why boolits quenched from the mold should be sized right after casting and oven heat treated boolits should be sized before heat treating.
Rick