Control of quantum coherence in a many-body system is one of the key issues in modern condensed matter, and conventional wisdom is that lattice vibration is an innate source of decoherence. Much research has been conducted to eliminate lattice effects. Challenging this wisdom, we show that lattice vibration may not be a decoherence source but an impetus of a novel coherent quantum many-body state. We demonstrate the possibility by studying the transverse-field Ising model on a chain with renormalization group and density-matrix renormalization group methods and theoretically discover a stable N = 1 supersymmetric quantum criticality with central charge c = 3/2. Thus, we propose an Ising spin chain with strong spin-lattice coupling as a candidate to observe supersymmetry. Generic precursor conditions of novel quantum criticality are obtained by generalizing the Larkin-Pikin criterion of thermal transitions. Our work provides the perspective that lattice vibration may be a knob for exotic quantum many-body states.