I am only seeing the black lines you refer to when viewing a face at grazing angles.
What fixed it for me was setting texture.aniostropy
in the loader callback function like so:
var map = object.children[0].material.map;
map.anisotropy = renderer.getMaxAnisotropy();
This, of course, is machine specific.
Otherwise, I do not see anything wrong with your model.
three.js r.56