One viable and cost-effective method to fulfill the ever-increasing mobile broadband traffic and to achieve coverage and capacity improvement is the employment of mobile small cells in next generation cellular networks. Being agile and resilient, aerial small cells (ASCs), which are small cells mounted on unmanned aerial vehicles (UAVs), are deemed promising platforms for the provision of wireless services. Since the lifetime of an airborne network highly depends on the residual battery capacity available to each ASC, it is essential to account for the energy expenditure on various flying actions in a flight plan. Therefore, the focus of this paper is to study the 3D deployment problem for a swarm of ASCs, in which a trade-off among flight altitudes, energy expenses and available lifetimes is observed. The objective is to maximize the total throughput of all users. We formulate the problem as a non-convex non-linear optimization problem and propose an energy-aware 3D deployment algorithm to resolve it with the aid of Lagrangian dual relaxation, interior-point and subgradient projection methods. We then conduct a series of simulations to evaluate the performance of our proposed algorithm. Simulation results manifest that our proposed algorithm can bring tremendous increase in the total throughput for all users by properly coping with the trade-off, compared to the two user-aware approaches with random and minimum altitude assignments.