It's stylistic. You can use either. "Said" isn't wrong.
Some writers feel very strongly about "bookisms," which is using words instead of "said" which tend to be more elaborate and give some action to speaking. (hissed, crooned, muttered, sighed, barked, laughed, snarled, grumbled) Personally I'm fine with them if they are used appropriately and judiciously, but your mileage may vary.
"Asked" isn't really a bookism, but it is a touch redundant (you pretty much only ask a question).
(Plus look, we're talking Tolkien, and linguistics professors can do whatever the hell they like with languages.)