This article establishes an approach, based on distributed optimization, for solving continuous-time Lyapunov equations (CTLE) over multiagent networks. Each agent in the network knows partial information of the CTLE and has a dynamical system to estimate exact or least-squares solutions. The aim of agents is to find a solution to CTLE by sharing information with connected agents over a network. This article develops distributed algorithms with an exponential rate of convergence for CTLE via the convex optimization design. Finally, this article presents numerical simulations to show the efficacy of the main results.