That is not done.
The acid is part of lead smelting anyway - lead sulphide its the usual ore: when visited a big lead smelters in france they were also smashing batteries and it all to the mix and dealing with the acid as part of their general processing.
"Galena, the most common mineral of lead, is primarily lead sulfide (PbS). The sulfide is oxidized to a sulfite (PbSO3) which thermally decomposes into lead oxide and sulfur dioxide gas. (PbO and SO2) The sulfur dioxide (like the carbon dioxide in the example above) is expelled, and the lead oxide is reduced. Anglesite, Cerussite, Pyromorphite, Mimetite and Wulfenite are other lead ores.
Other elements frequently present with lead ores include zinc and silver.[2]"