Closed-loop stability of nonlinear systems under real-time Lyapunov-based economic model predictive control (LEMPC) with potentially unknown and time-varying computational delay is considered. To address guaranteed closed-loop stability (in the sense of boundedness of the closed-loop state in a compact state-space set), an implementation strategy is proposed which features a triggered evaluation of the LEMPC optimization problem to compute an input trajectory over a finite-time prediction horizon in advance. At each sampling period, stability conditions must be satisfied for the precomputed LEMPC control action to be applied to the closed-loop system. If the stability conditions are not satisfied, a backup explicit stabilizing controller is applied over the sampling period. Closed-loop stability under the real-time LEMPC strategy is analyzed and specific stability conditions are derived. The real-time LEMPC scheme is applied to a chemical process network example to demonstrate closed-loop stability and closed-loop economic performance improvement over that achieved for operation at the economically optimal steady state. (c) 2014 American Institute of Chemical Engineers AIChE J, 61: 555-571, 2015