Perhaps Lewis was thinking of passages such as these as he wrote this.
1 Peter 2:1-2 (KJV): "Wherefore laying aside all malice, and all guile, and hypocrisies, and envies, and all evil speakings, As newborn babes, desire the sincere milk of the word, that ye may grow thereby."
1 Corinthians 3:2 (KJV): "I [Paul] have fed you with milk, and not with meat: for hitherto ye were not able to bear it, neither yet now are ye able."
Hebrews 5:12-14 (KJV): "For when for the time ye ought to be teachers, ye have need that one teach you again which be the first principles of the oracles of God; and are become such as have need of milk, and not of strong meat. For every one that useth milk is unskilful in the word of righteousness: for he is a babe. But strong meat belongeth to them that are of full age, even those who by reason of use have their senses exercised to discern both good and evil."
1 Corinthians 13:11 (KJV): "When I [Paul] was a child, I spake as a child, I understood as a child, I thought as a child: but when I became a man, I put away childish things."