Lead-Acid Battery: Standard Electrode Potential
Your reactions are wrong. 

$$\ce{Pb(s) + HSO^−_4(aq) -&gt; PbSO4(s) + H+(aq) + 2e−}$$
$$\ce{PbO2(s) + HSO^−4(aq) + 3H+(aq) + 2e− -&gt; PbSO_4(s) + 2H2O(l)}$$

Lead acid batteries are fairly reversible, hence their use as rechargable batteries. Anything that produces a gas, like in your reduction reaction, is unlikely to be reversible.