Mobile cloud offloading migrates heavy computation from mobile devices to remote cloud resources or nearby cloudlets. It is a promising method to alleviate the struggle between resource-constrained mobile devices and resource-hungry mobile applications. Caused by frequently changing location mobile users often see dynamically changing network conditions which have a great impact on the perceived application performance. Therefore, making high-quality offloading decisions at run time is difficult in mobile environments. To balance the energy-delay tradeoff based on different offloading-decision criteria (e.g., minimum response time or energy consumption), an energy-efficient offloading-decision algorithm based on Lyapunov optimization is proposed. The algorithm determines when to run the application locally, when to forward it directly for remote execution to a cloud infrastructure and when to delegate it via a nearby cloudlet to the cloud. The algorithm is able to minimize the average energy consumption on the mobile device while ensuring that the average response time satisfies a given time constraint. Moreover, compared to local and remote execution, the Lyapunov-based algorithm can significantly reduce the energy consumption while only sacrificing a small portion of response time. Furthermore, it optimizes energy better and has less computational complexity than the Lagrange Relaxation based Aggregated Cost (LARAC-based) algorithm.