According to the Donaldson, Tolkien's works (which he's read and admires greatly) was an influence for own writings works, but certainly not the only or even a key influence. On several occasions he mentions Heart of Darkness as being a more apt model.
Q. What, if any, connection is there between The Land and Middle Earth? There are some similarities between the two, is The Land homage to Middle Earth or is Middle Earth a model for what the Land is?
SD: Tolkien's work made what I do possible. In that sense, "Lord of the Rings" is an inspiring model for "The Chronicles of Thomas
Covenant." But Middle Earth itself was never a model for the Land
(except in the sense that Tolkien showed me what could be done within
the bounds of epic fantasy). Looking back, I can see "echoes" of
Middle Earth in the Land. But then, I can see "echoes" of lots of
things in the Land (Conrad's "Heart of Darkness" leaps to mind).
An interview with Stephen R. Donaldson
He also addresses the element of the ring being a key part of the book series and the general similarities within the fantasy genre.
Q. If a new reader came to you and said they'd heard of Thomas Covenant but didn't know much about the series, what would you say to describe it to them?
SRD: I consider this an impossible question. I'm the wrong person to
offer a reader's perspective on my own work. When people ask me,
"What's your book about?" I often say, "About 650 pages." What else am
I going to say?
But when the question is phrased differently, I sometimes say, "I'm
playing in the same ballpark as J.R.R. Tolkien, but he's playing
softball and I'm playing hardball." And sometimes I say, "Do you know
Tennyson's Idylls Of The King? I'm trying to accomplish the opposite."
In Tennyson, one pure, self-sacrificing, honorable hero--Arthur--is
eventually destroyed by his venal, petty, self-serving, or misguided
knights. I'm taking one weak, despairing, self-serving protagonist and
exploring the question of whether or not he can be redeemed by pure,
self-sacrificing, honorable companions.
Q That truly a hero's journey. And it has been a long, long road
to reach this point. Where did it all begin? Specifically, how did
Thomas Covenant come to exist?
SRD: I don't want to repeat the answer I usually give. After a while,
it becomes tedious. Instead I'll say this: During my "formative years"
(as an English major in college and graduate school), Lord Of The
Rings was at the height of its popularity, regularly selling a million
sets a year; but in my intellectual world those books were regarded
with what I'll call affectionate contempt. I was the only person I
knew who took them seriously, not as "a good read", but as literature.
As a result, I felt as alien and misguided among my peers as Covenant
first does in the Land. So now I think it's fair to say that I wrote
the first Chronicles in an effort to discover why I considered fantasy
important when no one else in my world did.
Interview: Stephen R. Donaldson and the Last Chronicles of Thomas Covenant: Ending the Tale of the Land
and
Q. Many fantasy writers consciously or unconsciously model their work on that of Tolkien and map their stories to Campbell's "Hero's Journey". I would suggest that you have not, rather pointedly. Would that be a fair assessment, or do you interpret these two influences differently?
SD: I don't actually know what Campbell had to say about the "Hero's Journey", so I can't claim that I was influenced, either positively or negatively. But I don't think of my work as a reaction against Tolkien's. In fact, I believe that he made what I do possible, and for that I will always be grateful. Instead I prefer to say that when he opened the door I walked through it.
I'll only give one example: THE RING (since that's the basis on which I'm sometimes dismissed as an imitator of Tolkien). Sure, Tolkien's ring is important in his story. But it's specific shape and substance aren't actually relevant to the personalities and dilemmas of the characters who carry it: since all they have to do is carry it and endure it or reject it, it could just as effectively be a torc, a bracelet, a necklace, an armband.
But in The Chronicles the ring as a ring takes on an entirely different kind of importance: as a symbol, first, of the voluntary commitments which people can make to each other, and, second, of the alloyed nature which defines and bedevils virtually every human being. (Which is probably why I consider my game hardball rather than softball.)
Interview: Stephen R. Donaldson and the Last Chronicles of Thomas Covenant: Ending the Tale of the Land