In the this work, we propose a two-layer approach to dynamic economic optimization and process control for optimal time-varying operation of nonlinear process systems. The upper layer, utilizing a Lyapunov-based economic model predictive control (LEMPC) system, is used to compute dynamic economic optimization policies for process operation. The lower layer, utilizing a Lyapunov-based MPC (LMPC) system, is used to ensure that the closed-loop system state follows the optimal time-varying trajectories computed by the upper layer over each finite-time operating window. To improve the computational efficiency of the two-layer structure, we allow both the LEMPC and the LMPC to compute control actions for two distinct sets of manipulated inputs thus decreasing the real-time computational demand compared to other one-layer EMPC schemes. Following a rigorous formulation and analysis of the proposed method, we demonstrate boundedness of the closed-loop system state and closed-loop economic performance improvement with the proposed two-layer framework compared to steady-state operation as well as with respect to other existing time-varying operating strategies previously proposed in the literature in the context of a benchmark chemical process application.