Well, she's been asked that question. From Wikipedia:
Rowling maintains that she hadn't read The Hobbit until after she completed the first Harry Potter novel (though she had read The Lord of the Rings as a teenager) and that any similarities between her books and Tolkien's are "Fairly superficial. Tolkien created a whole new mythology, which I would never claim to have done. On the other hand, I think I have better jokes."
And then, there is this quote:
"Me. I truly never sat down and thought, What do I think kids will like? I really, really was so inflamed by the idea when it came to me because I thought it would be so much fun to write. In fact, I don’t really like fantasy. It’s not so much that I don’t like it, I really haven’t read a lot of it. I have read “Lord of the Rings,” though. I read that when I was about 14. I didn’t read “The Hobbit” until I was in my 20s-much later. I’d started “Harry Potter” by then, and someone gave it to me, and I thought, Yeah, I really should read this, because people kept saying, “You’ve read ‘The Hobbit,’ obviously?” And I was saying, “Um, no.” So I thought, Well, I will, and I did, and it was wonderful. (Sheepish smile)
It didn’t occur to me for quite a while that I was writing fantasy when I’d started “Harry Potter,” because I’m a bit slow on the uptake about those things. I was so caught up in it. And I was about two thirds of the way through, and I suddenly thought, This has got unicorns in it. I’m writing fantasy!" (Jones, Malcolm. “The Return of Harry Potter,” Newsweek, 10 July, 2000)
I'd have to say that although she may not have consciously intended any parallel, having read the LoTR (as she admits) it's likely that it influenced her writing.
Again, from Wikipedia:
Tolkienian scholar Tom Shippey has maintained that "no modern writer of epic fantasy has managed to escape the mark of Tolkien, no matter how hard many of them have tried."
He makes a good point; it could be argued if she had never read them (although they influence many other works that she would have run across that it's still questionable), but since she admits that she DID, I think the LoTR series should be considered influences for Harry Potter.