According to the article, that's precisely what he did.
But he did it in a better way, randomly expanding ellipses. And when you're dealing with hundreds of dimensions, it's incredibly easy to be montecarlo-ing in the wrong directions...
I don't think so. You can't just "Montecarlo the hell" out of a post-quantum cryptographic scheme [1] which are also based on lattices. Even if that analogy isn't quite apt, I don't think looking for a good random lattice is a good way to find the densest possible lattice [2].
