No. It will not be possible to precipitate all lead ions from a solution by precipitating them with chloride.
Precipitation reactions
When a chloride salt is used to precipitate lead ions from a solution, an insoluble lead chloride salt would be formed
Pb2+ + Cl- ---> PbCl2
However, the formation of PbCl2 in an aqueous medium leads to the establishment of equilibrium between dissolved ions and undissolved solids.
PbCl2 (aq) <------> Pb2+ + Cl-
Thus, it will not be possible to completely remove all the lead ions from the solution.
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