Well now. this is a tricky one.
It might be useful to bring all the clues together.
If the first line is for the teeth, what would the second line involve?
The third and fourth lines vary: the fifth is for the nose...
The sixth line is for the weakest - it's made of the smallest and simplest...
We're all working on the assumption that its a poem, but Py hasn't said that.
If it is, then The third and fourth lines vary implies that its a poem with several verses and that the other bits apply to all the verses, which makes me think more of a song than a poem.
So, possibly a silly song like the one about Bombadil and the troll, or the song of the Ents and the Entwives, but neither of those fit the clues.
Nor anything else I can find in LOTR or the Silmarillion.
So then I thought of lines as lines of people in a battle, but what would that mean, and especially difficult is "for the nose"
Or line in a chart or a family tree, but again nose? and teeth?
I'm still persuaded by this lines of battle idea, with the sixth line being the smallest and the simplest.
Animals coming up at the last and hurling themselves at the enemy. There's definitely a memory there, but I can't quite catch it. Or an I thinking of Narnia or something?