I am making stats blocks for monsters from Middle Earth, and I'm trying to cover all the monster types. So far I have Giant Spider, Great Beast, Great Eagles, Wargs and Oliphaunts for beasts; Balrog/Maiar for celestials; Dragons for dragons; Shelob for fiends; Hill Trolls, Cave Trolls, Olog-Hai, and Stone Giants for giants; The free peoples, Goblins, and Orcs for humanoids; Fellbeasts, The Watcher in the Water, and Werewolves for monstrosites; Ents, Huorns, and Old Man Willow for plants; and Barrow-Wights and Nazgul for undead. I feel like I need more fiends, and I don't have any fey, abberations, elementals, oozes, or constructs. I was thinking of making Grond a construct, which wouldn't be to much of a stretch. Could anyone help me with finding creatures for the other types?

You should look at the prehistory of TLotR. In the Great War that Sauron lost when he first lost the ring Balrogs and worse walked Middle Earth.

Quote from IamSposta >>

You should look at the prehistory of TLotR. In the Great War that Sauron lost when he first lost the ring Balrogs and worse walked Middle Earth.

 I assume you mean the War of Wrath?

You can read about it in The Silmarillion and The History of Middle Earth volumes 1-5. I must admit to not having read all of that, but I know that they include a ton more lore about everything.

In LotR, elves actually act like fey, since they're native to the utter west. Tom Bombadil also strikes me as fey. For the balrog, you might as well just use the balor since they were ripped off from inspired by the former. They should be listed as fiends. Although they're of the same type as the wizards, they've warped by Morgoth into "umaiar" the same way demons were warped angels. Giant spiders should probably be listed under monstrosities. They're not natural, being descendants of Ungoliant. Vampires are also in the LotR canon, though they seem like werebats.

Thanks! These suggestions are very helpful. I'd be hard to create a statblock for vampires, though, as they only appear twice and aren't really described. 

You can just use statblocks. Giant spider - we already have that. Great eagles - giant eagles. Etc. Don't waste your time making loads of stuff when you can just use official ones that are there and match. But yes, LoTR is amazing, and seems a cool place to set an adventure.

Quote from BramblefootDruid >>

You can just use statblocks. Giant spider - we already have that. Great eagles - giant eagles. Etc. Don't waste your time making loads of stuff when you can just use official ones that are there and match. But yes, LoTR is amazing, and seems a cool place to set an adventure.

 The only difference with the spiders and eagles was increasing their intelligence and allowing them to speak Common. It only took about a minute with the statblock modfier tool that I use. Thank you, though. 

Ok, that makes sense. Hope your campaign goes well!