In this research, a sustainability and cost assessment of battery health management strategies applied to Lithium batteries of an electric Unmanned Aerial Vehicle (eUAV) is performed. A mission-based strategy is proposed with the aim to elongate battery lifetime. With this strategy, the battery is charged to the estimated State of Charge (SOC) level required to complete the next flight. The mission-based strategy is compared to two other strategies: the SOC 100% strategy that always fully charges the battery before flight, and, the SOC 80% strategy that charges that battery to 80% before flying. The three strategies are tested for a variety of flight distances. The battery model is simulated using Python Battery Mathematical Modelling (PyBaMM). A Monte Carlo (MC) simulation is run to review the response to uncertainties in initial battery compositions and operating conditions. Ultimately, the strategies are evaluated on environmental impact, financial costs and flying efficiency. The results show that the mission-based strategy outperforms the SOC 100%, yielding lower emissions and costs and higher flying efficiency performance. However, depending on the range flown, the SOC 80% shows environmental, cost and flying efficiency benefits that challenge the relevance of implementing a mission-based battery health management strategy.