He wasn’t a theologian.
He was a devoutly Christian Protestant thinker and writer. https://www.patheos.com/blogs/getreligion/2013/11/concerning-c-s-lewis-christian-apologist-not-theologian/
People who understand his writings well understand he was not a theologian nor did he ever claim to be one.
systematics is only one part of theology. In it purest form theology translates as the study of God. Lewis certainly did that and communicated his conclusions to n a way that has touched millions. One does not need a formal degree to be a theologian