A concise and factual abstract is required. The abstract should state Target coverage and lifetime maximization problems are major challenges for mobile wireless sensor networks (MWSN). In this paper, we propose a Multi-Objective formulation for MaxiMizing lifetime with Target Coverage called MO-MMTC, which accounts for the energy fluctuation among mobile sensors after each movement. We prove the formulation to be NP-hard and propose the Enhanced Non-dominated Sorting Genetic Algorithm II (ENSGA-II), a multi-population genetic algorithm, to solve this problem. Experiments are performed to compare ENSGA-II with TV-Greedy, an existing state-of-the-art heuristic for MMTC. Our results show that the proposed algorithm significantly improves many evaluation metrics compared to baseline methods.