Indeed. Both were members of “The Inklings”, a group of literary enthusiasts who met at Oxford. Owen Barfield (author of Saving the Appearances: a Study in Idolatry and other books) and Charles Williams (author of The Place of the Lion and other novels) were also regulars in the group.
I was reading “The Consolation of Philosophy” by Boethius and ran across the word “inkling” in the translation I was reading. I immediately thought of Lewis! I know he read that book with its beautiful poetry and profound theology and it occurred to me that this may have been an influence to the adoption of that peculiar name for his group. I really need to research it....it is of interest to me.