Regarding MacBeth/LOTR, certainly there is a superficial resemblance to MacBeth in a different subplot of LOTR: The fight between the ents and Saruman. The ents marching on Isengard certainly is reminiscent of Birnham wood (used as camouflage) marching toward MacBeth's castle. Of course, there isn't any equivalent prophesy "Saruman shall never be overthrown, not until the trees of Fangorn forest march within the circle of Isengard." (that might have been to obvious a Shakespeare reference for Tolkien's taste)
The Witch-King and Eowyn story is in the general category of prophesies and their misinterpretation (not seeing the loopholes!!) MacBeth is a famous example of this, but there are many others, going back (at least) to ancient Greece.
One other (inadvertant) bit of irony involving the WK, when he tells Gandalf "this is my hour!" As someone pointed out in another thread,
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it was his hour, just not in the way he had hoped.
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