Reaction on positive electrode (cathode): PbSO₄₍s₎ + 2H₂O₍l₎ → 2e⁻ + PbO₂₍s₎ + 4H⁺₍aq₎ + SO₄²⁻₍aq₎. s - solid. l - liquid. aq - dissolve in water. PbSO4 is converted to Pb at one electrode (anode) and to PbO₂ at the other (cathode). Lead battery can be recharged, during recharging, an external source of energy is used.
Pb +SO42- -> PbSO4 + 2e- is the reaction that occurs at the anode when discharging. So, when recharging, this reaction occurs at the cathode, but in reverse.