You'd be better off with the old World of Darkness for this but as the others have said, it can be done. Some of the books for the new Changeling: the Lost might also help alongside Mirrors given that they have thematically suitable critters in and a style of magic suitable to the setting but are far from essential.
Keep mostly to the basic human rules of the core book for characters, most Middle earth races don't have the vast power lists that either WoD is built around. You can do a lot with simple modifiers to the basic stats (+1 appearance and a higher maximum dexterity for elves etc, +1 to horse riding for the men of Rohan ...). Have some skills restricted to give flavour to the races (Hobbits are not well traveled, Dwarves are good at mining etc). Then tweak your merits to fit the setting.
Most kewl powerz in the hands of the player characters won't be from actual supernatural or magical skills but from fixed objects; swords that glow when a certain critter is near, rings that turn you invisible, daggers that break and slowly poison the victim. You should be able to stat these up before play and steal ideas and examples from the variety of powers in the various books. Steal a vampires power and attach it to a sword, use the Prometheans power as the effect of an elven potion etc.