Lead chloride is somewhat soluble in cold water
0.67 grams of lead (II) chloride PbCl2 is soluble in water at 0 degrees C.
0.98g/100g H2O @ 20 deg C.
1.08g/100g H2O @ 25 deg C.
1.19g/100g H2O @ 30 deg C.
1.32g/100g H2O @35 deg C.
1.78g/100g H2O @ 50 deg C.
2.13g/100g H2O @ 65 deg C.
2,62g/100g H2O @ 80 deg C.
3,25g/100g H2O @ 100 deg C.
So with very hot water (soaking wash), we can dissolve a couple of grams of lead chloride--decanting the solution while hot (with all of the silver chloride settled), letting this wastewater cool to lower the solubility of the lead chloride, when cool return the water (leaving most of the lead salt behind) to pick up more lead chloride from your reaction vessel with a reheat, repeat this until you no longer get the needle-like PbCl2 crystals in the cooled wash water.
Silver chloride is white and fluffy or milky can be hard to settle it likes to move around easily in solution. So you may have to lower heat from a rolling or bubbling and give the silver salt some time to settle when you remove lead chloride...
Silver chloride is insoluble in cold or hot water or in acid.
Tin (is just a problem ), some of the soluble tin salts will be washed out with the lead and the hot water washes above, the hot water washes can also promote further oxidation of the tin salts that and exposure to air or other conditions you could have a variety of tin salts or oxides involved.
SnCl2 is soluble in water, about 98g SnCl2/100g H2O @ 20 deg C. and stannous chloride is very soluble in HCl acid.
SnCl4 stannic chloride (hydrolyzes in water) soluble in concentrated. 20% HCl.
but you are more likely to have other oxides of tin such as;
SnO2 tin (IV) oxide stannic insoluble in water, soluble in concentrated HCl (hydrolyzes to goo in dilute of cold solutions)
Sn(OH)2 stannous hydroxides insoluble in water, but soluble in concentrated 20% HCl.
Sn(OH)3 stannite (Normally made from SnO or some other tin salt or tin oxide reacted with a strong base), soluble in strong HCl...
Tin chloride salts in a warmer more concentrated acid solution will form a little less of the jelly-like goo, tin chloride salts in dilute solution or water hydrolyze to give more trouble in filtering...
Water washes after acid washes will remove more salts and in some cases make the salts easier to oxidize, lowering the acid involved...
Many of the other base metal chlorides will also be soluble in the hot water washes or in the HCl washes...
We can go different ways from this point to get the silver (through a complex) as an ammonium complex in which there is a danger of making an explosive compound if not carefully performed properly, (acidified to recover silver and make safer), there is also thiosulfate which can dissolve silver...
Because of the chloride salts involved, we would not want to go straight to nitric acid at this point (unless our goal was to put gold into solution), the silver chloride insoluble in the acid.
Silver chloride salts, along with the other base metal chloride salts, would put some gold into solution as the base metal chloride reformed HCl in solution with the gold and nitric acid...
With fine gold or foils, we can dissolve the gold in a chloride solution without using nitric, we can use hypochlorites or H2O2...
Silver chloride is insoluble in aqua regia where the gold is soluble...
Or in a gold chloride solution made sodium hypochlorite or H2O2 or some other suitable oxidizer...
Or
We can wash the insoluble silver and base metals salts in a solution of NaOH this will lower some of the acidity, help oxidize some of the base metals (may dissolve some of the more amphoteric base metals along the way), and help us to convert base metal chlorides to sodium chloride salt (table salt) that can be washed with water, drying these salts they can be fused ( to further drive off acids and convert to oxides, and then roasted in a red heat fine powders stirred well and well exposed to oxygen or atmospheric air to complete the conversion of base metals ready for most any acid like nitric...
Edited to add a little info and grammar corrections as best I could.