Lucas's argument that reasoning presupposes freedom is if determinism is true we would accept the arguments in conditioned reflexes. We would have no freedom and our process of reasoning would be determined. If people believe that reason does not exists, it basically means that we do have free will and are not determined. I believe with it because when humans are capable of reasoning with their own ideas and we are able to choose what is right or wrong. Our ideas, to ourselves, are trustworthy and acceptable.
Freedom is crucial to humanity. Without it, we would all be "locked in a cage" (a common argument against fascism). Please do NOT get me wrong, I think reasoning is completely imperative to life (even more so than blind emotion), but there can be no reasoning without freedom. Think of propaganda, for example.