We study causality in systems that allow for feedback loops among the variables via models of cross-sectional data from a dynamical system. Specifically, we consider the set of distributions which appears as the steady-state distributions of a stochastic differential equation (SDE) where the drift matrix is parametrized by a directed graph. The nth-order cumulant of the steady state distribution satisfies the corresponding nth-order continuous Lyapunov equation. Under the assumption that the driving Lévy process of the SDE is not a Brownian motion (so the steady state distribution is non-Gaussian) and the coordinates are independent, we are able to prove generic identifiability for any connected graph from the second and third-order Lyapunov equations while allowing the cumulants of the driving process to be unknown diagonal. We propose a minimum distance estimator of the drift matrix, which we are able to prove is consistent and asymptotically normal by utilizing the identifiability result.