The lattice is latent space pushed through f into observation space; f squashes one axis by ℓ (forward Lipschitz is the easy, cheap direction). Now go backwards: a fixed little observation gap d (teal) has to be explained by a latent gap of size d/ℓ — the orange needle. With healthy ℓ it's a tidy ball you can trust. Drag ℓ toward 0 and the needle explodes: a tiny observed difference could mean an enormous latent move, so you can't read the latent off the observation. That co-Lipschitz lower bound — not the easy upper one — is the whole crux of the idea.