Tank leaching is a good separation method for concentrate. In addition, Ag ions in the solution can be aid to leach from concentrate by prevent the formation of jarosite.
The high grade PbS concentrate would typically be treated via the pyro metallurgical route.
However assuming that the PbS is finely ground then leaching is possible. Oxygen leaching to convert the PbS to sulphate is not feasible due to the low solubility of lead sulphate.
This means that leaching with nitric acid (probably) is required to oxidise the lead and solubilise it as a nitrate. Conversion to lead chloride and recovery of the nitric acid is then possible. Not sure if hydrochloric acid can leach the PbS directly.
The problem will be the by-products, ie iron, silica, sulphur etc. I would expect that recovery of the silver and lead can be achieved, the temperatures etc will depend on the kinetics.
Ps I don't know if this is done on an industrial scale as it seems at face value this would be too hard and hazardous when compared to the smelting route. The cost of processing on any significant scale may also render it uneconomic.
Using Slurry Electrolysis Process. CaCl2 300g/L, pH=2~3(HCl), 60℃. I have done this work ten year ago.You can see my paper: Technological research on complicated antimony-lead concentrate Slurry Electrolysis.