During one of the discussions of the Chronicles of Amber, the question arose whether Zelazny thought about creating an analogue of The Lord of the Rings, and how much did Tolkien influence him? Did Roger Zelazny know about The Lord of the Rings at all? Perhaps in the '60s it was not as widely known as it is now. Is there any evidence of his acquaintance with The Lord of the Rings, any commentaries on this?
In a 1973 interview with Zelazny reprinted in the Roger Zelazny book from the Modern Masters of Science Fiction series, and partly available on google books here, he is asked to name masters of SF/Fantasy on this page and he includes Tolkien, so it's safe to say he read him:
GEIS: Who do you consider the finest sf and/or fantasy writers alive and working today? Why?
ZELAZNY: Hard to say. My tastes vary and so does any writer's output. This in mind, the best? In no particular order, then: Clarke, Le Guin, Dick, Tolkien, Heinlein, Niven, to name the first half-dozen fine ones who come to mind.
Why? De gustibus, is all.
On the other hand, in the interview here published in the January 1969 issue of Worlds of If, he talks about a bunch of authors that influenced him and doesn't mention Tolkien, so either he hadn't read him yet or perhaps didn't consider him a major influence on his own writing.
@KlausÆ.Mogensen also points to this Zelazny interview where he cited various non-Tolkien influences on the Amber books specifically:
I have been asked on numerous occasions whether the Amber books were influenced by Jessie L. Weston's 'From Ritual to Romance', by Philip Jose Farmer's 'World of Tiers' novels, by Celtic mythology and Arthurian legend. The answer to all of these, in varying degrees, is yes.