Here's the payoff of the lower bound. You measured an observation gap d between predicted and real. The co-Lipschitz bound guarantees the true latent correction lives inside a ball of radius d/ℓ around your current latent (white dot) — a certificate, not a guess. The orange dot is the real correction; it is provably inside. With a decent ℓ the ball is tight and you can fix the latent without searching. Shrink ℓ and the ball swallows the whole space — the certificate goes vacuous. This is what turns "fix the latent" from blind search into a bounded, guaranteed region.