While stability analysis is a mainstay for control science, especially computing regions of attraction of equilibrium points, until recently most stability analysis tools always required explicit knowledge of the model or a high-fidelity simulator representing the system at hand. In this work, a new data-driven Lyapunov analysis framework is proposed. Without using the model or its simulator, the proposed approach can learn a piecewise affine Lyapunov function with a finite and fixed offline dataset. The learnt Lyapunov function is robust to any dynamics that are consistent with the ofline dataset, and its computation is based on second-order cone programming. Along with the development of the proposed scheme, a slight generalization of the classical Lyapunov stability criteria is derived, enabling an iterative inference algorithm to augment the region of attraction.