J. R. R. Tolkien
The request for a sequel prompted Tolkien to begin what would become his most famous work: the epic novel "The Lord of the Rings" (originally published in three volumes 1954–1955). Tolkien spent more than ten years writing the primary narrative and appendices for "The Lord of the Rings", during which time he received the constant support of the Inklings, in particular his closest friend C. S. Lewis, the author of "The Chronicles of Narnia". Both "The Hobbit" and "The Lord of the Rings" are set against the background of "The Silmarillion", but in a time long after it.
Charles Williams (British writer)
Although Williams attracted the attention and admiration of some of the most notable writers of his day, including T. S. Eliot and W. H. Auden, his greatest admirer was probably C. S. Lewis, whose novel "That Hideous Strength" (1945) has been regarded as partially inspired by his acquaintance with both the man and his novels and poems. Williams came to know Lewis after reading Lewis's then-recently published study "The Allegory of Love"; he was so impressed he jotted down a letter of congratulation and dropped it in the mail. Coincidentally, Lewis had just finished reading Williams's novel "The Place of the Lion" and had written a similar note of congratulation. The letters crossed in the mail and led to an enduring and fruitful friendship.