While it is an interesting theory, it was actually influenced by a slightly different legendarium(s) than Tolkien's. From Green Lantern Wiki:
The first appearance of a power ring was in All-American Comics #16 (July 1940), the flagship title of comic book publisher All-American Publications, which featured the first appearance of Alan Scott.
Green Lantern's original alter ego was Alan Ladd, a play on the name Aladdin, until a conflict arose regarding the actor Alan Ladd. Creator Marty Nodell has cited Richard Wagner's opera cycle The Ring of the Nibelungen and the sight of a trainman's green railway lantern as inspirations for the combination of a magical ring and lantern. (src: Martin Nodell, Preface to The Golden Age Green Lantern Archives volume 1, 1999)
It has been claimed that another original inspiration for the Silver Age interpretation of Green Lantern was the Lensman series, a serial science fiction space opera, by E.E. "Doc" Smith, but the creators have vehemently denied this claim.
So, it was mostly the Nibelungen ring that influenced the Green Lantern ring.
As a side note, for those tempted to say "well, probably Nibelungen ring influenced Tolkien, so the 2 works are more siblings than ancestral", that is not the case. Nibelungen Wiki states:
J. R. R. Tolkien's fantasy novel The Lord of the Rings (1937-1949) shares elements with Der Ring des Nibelungen; however, Tolkien himself denied that he had been inspired by Wagner's work, saying that "Both rings were round, and there the resemblance ceases". (Source: Tolkien, J.R.R. (1981). "Letter 229". In Carpenter, Humphrey; Tolkien, Christopher. The Letters of J.R.R. Tolkien. Boston: Houghton Mifflin. ISBN 0-395-31555-7.)