Lorentz symmetry is a fundamental symmetry of Nature, and if at smallest scale, the symmetry is broken, as many suggestions to the theories of quantum gravity would "naturally predict", there is a long-standing puzzle how one can acquire Lorentz symmetry as an emergent symmetry at extremely high precision at low energy. We show that coupling the Standard Model to a Lorentz symmetry violating sector may co-exist with viable phenomenology, provided that the interaction between the two is mediated by higher-dimensional operators. In particular, if the new sector breaks Lorentz symmetry by acquiring anisotropic scaling behavior above a "Horava-Lifshitz" energy scale $Lambda_L$ and couples to the Standard Model through interactions suppressed by the Planck mass $M_p$, the transmission of the Lorentz violation into the Standard Model is protected by the ratio $Lambda_L^2/M_p^2$. A wide scale separation, $Lambda_L<<M_p$, can then make Lorentz-violating terms in the Standard Model sector within experimental bounds without fine-tuning. We first illustrate our point by a toy example and then explain that the proposal unfortunately does face some difficulty due to the existence of instantaneously propagating non-Lifshitz modes in gravity.