Lead chloride is sparingly soluble in hot water, so washing with that should remove limited quantities.
EDIT: As Lou originally posted; if there is a lot of lead in the precipitate, precipitating everything as chloride, washing the chloride with water, then selectively dissolving the silver chloride with ammonia, discard the undissolved lead chloride (in an environmentally responsible way), re-acidify the ammoniacal solution with more hydrochloric acid is the way to go.
.... the silver chloride should become quite clean from that procedure, by the way!
How much lead do you have in your alloy?
Iron is rather bad for the reduction, anything more noble than iron will also be reduced to the metallic state, and iron is a bad contaminant in silver alloys for jewellery.
A better approach would be to precipitate as chloride, wash thoroughly with several batches of boiling water (until no PbCl2 precipitates from the wash-water on cooling, or a test with potassium iodide is negative), then reduce with zinc or aluminium.
Or even better:
"Cement" with copper, thus leaving anything less noble than copper in the solution (including the copper), wash, dry and melt the silver powder.
The second approach will give a far better product than reducing with iron, and should you then run the silver in a silver cell, the result will be very fine silver. (99.99 or 99.999)