What should be the reaction between lead oxide and dilute sulfuric acid?
YOur logic is wrong.


  I know for a fact that dilute $\ce{H2SO4}$ is a non-oxidizing acid...


sort of, but so far so good.


  ...which makes it a reducing agent.


This is where you are wrong, just because it is non-oxidizing does not make it reducing. Concentrated $\ce{H2SO4}$ is an oxidizer, diluting it does not make it less of an oxidizer, but limits the strength/mechanism.

A similar example is mixing nitroglycerin and diatomaceous earth doesn't make nitroglycerin less explosive, it just makes it harder for it to explode (dynamite).