This paper studies a nonlinear predictive energy management strategy for a residential building with a rooftop photovoltaic (PV) system and second-life lithium-ion battery energy storage. A key novelty of this manuscript is closing the gap between building energy management formulations, advanced load forecasting techniques, and nonlinear battery/PV models. Additionally, we focus on the fundamental trade-off between lithium-ion battery aging and economic performance in energy management. The energy management problem is formulated as a model predictive controller (MPC). Simulation results demonstrate that the proposed control scheme achieves 96%–98% of the optimal performance given perfect forecasts over a long-term horizon. Moreover, the rate of battery capacity loss can be reduced by 25% with negligible losses in economic performance, through an appropriate cost function formulation.