The chemistry is that lead corrodes rapidly in the presence of excess oxygen, which is provided by the hydrogen peroxide, and the resultant lead oxide is very soluble in a weak acid, the white vinegar.
The downside is that you should not use it in aluminum cans as it will tend to corrode the aluminum as well as the lead. Of course the byproduct of this reaction is lead acetate, a very toxic compound which can be absorbed through the skin and the disposal of the used mixture must be done carefully.
Some people just keep the used solution in a 5 gallon jug and put it out when their local garbage collectors do a Haz-mat garbage day where people dispose of their old paint and poisons, etc. Where I live they do it oce a year.