This is from Lewis:

"Before leaving the question of divorce, I should like to distinguish two things which are very often confused. The Christian conception of marriage is one: the other is quite the different question—how far Christians, if they are voters or Members of Parliament, ought to try to force their views of marriage on the rest of the community by embodying them in the divorce laws. A great many people seem to think that if you are a Christian yourself you should try to make divorce difficult for every one. I do not think that. At least I know I should be very angry if the Mohammedans tried to prevent the rest of us from drinking wine. My own view is that the Churches should frankly recognize that the majority of the British people are not Christian and, therefore, cannot be expected to live Christian lives. There ought to be two distinct kinds of marriage: one governed by the State with rules enforced on all citizens, the other governed by the church with rules enforced by her on her own members. The distinction ought to be quite sharp, so that a man knows which couples are married in a Christian sense and which are not."

"It's what people like him would do" is just plain false. He is quite clear there that the fact that he does not want to ban divorce for other people is not arbitrary, but reasoned, and he would apply the same thing to anything else which was specific to his religion.