I don't think the ability to compartmentalize is what Lewis meant there. He is not arguing that Christ, if only a man, could not have been inconsistent.
He is arguing against the rather common and condescending notion that Christ was a great, humble, moral teacher. He argues that Christ purposefully took this off the table as an option. His teachings were not humble (as in John 8:58, my favorite verse in all of scripture where Christ states that "before Abraham was, I AM!"), and if you listen to his words and believe that he was not the Son of God, you must decide whether He was a liar, or a nutjob. You cannot call yourself the Son of God, "I AM", and claim to exert the authority that Christ did, and be a good teacher, if you are not God.
Your counter-argument is logical, but Christ's positions and His rationale for the Authority to hold them are not easily seperated in the record. To do so, to strip away his divinity and look only at his more universally accepted moral teachings, He then MIGHT be a moral teacher, but I would argue, not a "great" one.
I think Josh McDowell expanded on this in "More Than a Carpenter", another must read for introductory Apologetics. My favorite author in Apologetics is a tie between Lewis and Norman Geisler. Geisler is more theologically learned, but Lewis far more poetic.
See my post nr. 60...
I think people who love the teachings of Christ should not be condemned, but rather encouraged.
A dear friend of me brought me to Christ that way...