An ideal embodied agent should possess lifelong learning capabilities to handle long-horizon and complex tasks, enabling continuous operation in general environments. This not only requires the agent to accurately accomplish given tasks but also to leverage long-term episodic memory to optimize decision-making. However, existing mainstream one-shot embodied tasks primarily focus on task completion results, neglecting the crucial process of exploration and memory utilization. To address this, we propose Long-term Memory Embodied Exploration (LMEE), which aims to unify the agent's exploratory cognition and decision-making behaviors to promote lifelong learning. We further construct a corresponding dataset and benchmark, LMEE-Bench, incorporating multi-goal navigation and memory-based question answering to comprehensively evaluate both the process and outcome of embodied exploration. To enhance the agent's memory recall and proactive exploration capabilities, we propose MemoryExplorer, a novel method that fine-tunes a multimodal large language model through reinforcement learning to encourage active memory querying. By incorporating a multi-task reward function that includes action prediction, frontier selection, and question answering, our model achieves proactive exploration. Extensive experiments against state-of-the-art embodied exploration models demonstrate that our approach achieves significant advantages in long-horizon embodied tasks. Our dataset and code will be released at https://wangsen99.github.io/papers/lmee/