Bill, I do a lot of casting with mostly pure lead for balls, which by the way actually has a BHN of about 4.7 not the 5 that is usually quoted,along with lead/tin and lead/tin/antimony alloys for rifle and pistol bullets.
I have and use two lead hardness testers, one from LBT and one from Lee to accurately compare hardness yields.
Pure lead is not effected by water quench or impact hardening that I can measure.
Lead/tin and lead/tin/antimony alloys will age harden for about two weeks after casting and then the lead/tin mix will spontaneously soften a few points after a year.
I'm told but have not tested that lead/tin alloys can be kept frozen to slow the age soften process that happens at about a year after casting.
Water dropping lead/tin mixes does not seem to have much effect if any. Also Tin alone will only harden a bullet to about 9-10 BHN then your just wasting tin as it will not go any higher without antimony which establishes a micro-crystalline structure known as "trees" that serve to harden and strengthen the alloy.
Lead/tin/antimony alloys will greatly harden to a water drop ( up to a BHN of about 40) is possible with oven heat treat and water quench.
Antimony alloys of about wheel weight consistency will water drop to a BHN of 12-14 and hold their hardness for many years.
I have some pistol bullets in cans I cast over 15 years ago that are still within a point or two of original BHN measurements.