C. S. Lewis wrote in Christian Reunion:
The real reason, I take it, why you cannot be in communion with us is not your disagreement with this or that particular Protestant doctrine, so much as the absence of any real "Doctrine", in your sense of the word, at all. It is, you feel, like asking a man to say he agrees not with a speaker but with a debating society.
And the real reason why I cannot be in communion with you is not my disagreement with this or that Roman doctrine, but that to accept your Church means, not to accept a given body of doctrine, but to accept in advance any doctrine your Church hereafter produces. It is like being asked to agree not only to what a man has said but to what he's going to say.
To you the real vice of Protestantism is the formless drift which seems unable to retain the Catholic truths, which loses them one by one and ends in a "modernism" which cannot be classified as Christian by any tolerable stretch of the word. To us the terrible thing about Rome is the recklessness (as we hold) with which she has added to the depositum fidei - the tropical fertility, the proliferation, of credenda. You see in Protestantism the Faith dying out in a desert: we see in Rome the Faith smothered in a jungle.
I know no way of bridging this gulf.
That said, Lewis usually takes great pains to avoid sectarian division (perhaps influenced by growing up in Northern Ireland), and is often sympathetic to Catholic viewpoints. For example, he received advice on Mere Christianity from Catholics as well as Protestants before its publication, to ensure that it expressed sentiments that were universally agreeable.
The book C. S. Lewis and the Catholic Church by Joseph Pearce (Ignatius Press, 2003) explores the development of Lewis's thought on this matter. The foreword by Thomas Howard summarises as follows:
Lewis wishes us to accept his identity as a "mere" Christian; but we find the truth of the matter is that he is a mere Protestant. [...] But there are more anomalies. Although he loathed the whole business of "High", "Broad" and "Low" churchmanship in the Church of England, he could not avoid it all. He had nothing but contempt for the Broad churchmen who diluted the Faith until it was a mere sickly gruel (see his Anglican bishop in The Great Divorce). And he detested the "smells-and-bells", lace-cotta, biretta sort of thing that one finds at Anglo-Catholic shrines, and which formed the metier of T. S. Eliot. He just wanted to be left alone, to go to church and be done with it.
But it was not so simple. In spite of himself, Lewis moved more and more toward what can only be called a "catholic" Anglicanism. Again - he hated the epicene punctilio of the Anglo-Catholic party: but his faith came to embrace all sorts of doctrines and practices that his evangelical readers (who are his most enthusiastic clientele) must sedulously ignore. He spoke of "the Blessed Virgin", and made his confession to his priest regularly, and believed in purgatory, and even came to refer to the Eucharist as - heaven help us all - the Mass! Lewis's anti-Romanism remained with him until his death, however.