John Bellairs: "The Face in the Frost" (1969)
Leigh Brackett (as early as 1943 to as late as 1971, but I believe most of her works were written prior to LOTR, but I will have to check my facts on that).
Fredric Brown (~ 1941 to 1963)
Edgar Rice Burroughs: "Pellucidar" Series (1922 -1941), Mars Series (1917 -1941), Venus Series (1934 - 1946)
Lin Carter: "World's End" Series (1969 - 1978)
L. Sprague de Camp: "Lest Darkness Fall" (1941), "Fallible Fiiend" (1973), et al. (many pre- 1966 works).
de Camp & Pratt: "Harold Shea" Series (1941 - 1953), "Carnelian Cube" (1948)
August Derleth (~1934 to 1961)
Lord Dunsany (~1915 - 1957)
P.J. Farmer: "The World of the Tiers" Series (begun in 1965, so I'll let it stand), et al. (many pre-1966 works)
Gardner Fox: "Kothar" Series (begun 1969), "Kyrik" Series (begun 1975), et al. (five works written prior to 1966)
R.E. Howard: "Conan" Series (Howard killed himself in 1936).
Sterling Lanier: "Hiero's Journey" (begun 1973).
Fritz Leiber: "Fafhrd & Grey Mouser" Series, et al. (F.L. published his first Fafhrd and Grey Mouser story in 1939 and continued publishing those and many other stories until his death in 1992; I've read enough of his literature to say without a doubt he didn't become a Tolkien imitator after the publication of any of Tolkien's works).
H.P. Lovecraft (died in 1937).
A. Merritt: "Creep, Shadow, Creep", "Moon Pool", "Dwellers in the Mirage", et al. (He died in 1943).
Michael Moorcock: "Stormbringer", "Stealer of Souls", "Hawkmoon" Series (esp. the first three books). M.M. will take further thought and investigation. He published his first Elric tale in 1961. I've read enough of his literature to say that despite the fact he no doubt has read Tolkien, I don't believe it influenced him, but I will leave his name un-bolded for now.
Andre Norton (A.N. published as early as 1934 and was with us until 2005. While I have read some A.N., I have not read enough to make an informed opinion. For now, she is off the list).
Fletcher Pratt: "Blue Star", et al. (Died 1956).
Fred Saberhagen: "Changeling Earth" (1973), et al. (some pre - 1966 work, but not much).
J.R.R. Tolkien: "The Hobbit", "Ring Trilogy"
Jack Vance: "The Eyes of the Overworld" (1966, however part of a series started in 1950), "The Dying Earth" (begun 1950), et al. Luckily, Mr. Vance is still with us as of the writing of this list. He began publishing in 1950.
Stanley Weinbaum (died 1935).
Manly Wade Wellman (began publishing in 1927).
Jack Williamson (began publishing in 1928).
Roger Zelazny: "Jack of Shadows", "Amber" Series, et al. (most of his work was published from 1970 onwards, but I have to say there is a definite lack of Tolkien influence in his works).
The appendix notes that de Camp & Pratt, REH, Fritz Leiber, Jack Vance, HPL, A. Merritt had particularly significant input to the game.