Technically, annealing means to draw all the hardness possible from a metal, and for lead alloys that requires about 350 degrees F, and a slow cooldown.
Boiling water would be classed more as a draw, or removal of part of the hardness, and with any draw, cooling rate isn't critical, but draw time at temperature has a strong influence on final hardness, with lead alloys. i.e. Just bringing to a boil and letting cool removes less hardness than boiling for an hour or two.
Understand that I speak as one with considerable experiance heat treating ferrous tool steel. Since there are similarities in process, I like to keep all the wording the same.
