Lifshitz scaling is an anisotropic scaling where time and space scale differently. Quantum field theories that exhibit Lifshitz scale symmetry provide a framework for studying low energy systems with an emergent dynamic scaling such as quantum critical points. Introducing supersymmetry to the Lifshitz algebra leads to a rich structure that is less constrained compared to that of relativistic supersymmetry. We construct holomorphic supersymmetric Lifshitz quantum field theories and study their renormalization properties, RG flows and spontaneous symmetry. We show that the theory exhibits non-renormalization theorems in a way which resembles the relativistic Wess-Zumino model in four dimensions. We show that in various cases of spacetime dimensions and marginal supersymmetric interactions, the theory possesses a line of quantum Lifshitz fixed points in which there is an exact Lifshitz scaling symmetry.