Except that Lewis' Christianity was not based on any authority deemed infallible. He reasoned himself into it, while recognising the fallibility of reason. His writings set out his arguments; they do not tout any source of authority whose reliability he has not already argued.

But how can one rightly reason, while recognising one's fallibility? That is an issue for rationalists as well.

Let me fix the original quote for you:

When we exhort people to Faith as a virtue, to the settled intention of continuing to believe certain things, we are not exhorting them to fight against reason. The intention of continuing to believe is required because, though Reason is perfect, human reasoners are not. When once passion takes part in the game, the human reason, unassisted, has about as much chance of retaining its hold on truths already gained as a snowflake has of retaining its consistency in the mouth of a blast furnace.

When a long argument produces a conclusion that strikes one as absurd, one sometimes just has to say, "This is bullshit. I don't know what's wrong with the argument, but I'm not going along with it."