He correctly states that time does not make our sins go away, or become less horrible. Just because the sin you're remembering happened twenty years ago doesn't mean you're not still just as guilty of it.
He goes on to say that perhaps the sins of our lives become public knowledge, and follow us into eternity. Here, I think he is mistaken. He does recognize that our sins are washed away in confession and in the blood of Jesus. But I think Lewis hangs onto those sins anyway, perhaps misunderstanding how God could be eternally present to all times along the timeline, and yet completely forgive our sins. Lewis's idea of heaven being so "public" a place I think takes too little into account of the idea contained in the verse where He says He casts our sins into the sea, to forget them.
Our sins do have consequences. But His redemption is complete. I don't think we'll forever be haunted by the sins of our brief lifetime.
In any case, we know that our joy on that day will be so complete that our suffering now will seem like nothing. So thanks be to God whether Lewis is right or wrong.
Thanks God, for making all things well.