The present disclosure relates to systems and methods by which lead from spent lead-acid batteries may be extracted, purified, and used in the construction of new lead-acid batteries. A method includes forming a first mixture in a first vessel, wherein the first mixture includes a lead-bearing material and a carboxylate source, which react to precipitate lead salt particles. The method includes separating a portion of the first mixture from a remainder of the first mixture, wherein the portion includes lead salt particles having specific densities below a specific density threshold value and/or having particle sizes below a particle size threshold value. The method includes forming a second mixture in a second vessel, wherein the second mixture includes the lead salt particles from the separated portion of the first mixture. The method further includes separating the lead salt particles of the second mixture from a liquid component of the second mixture.