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Here, we present LEMO Agent, a large-language-model agent framework for closed-loop inverse design of gas-separation MOFs in MOFid space. LEMO Agent couples language-based candidate generation with MOFid standardization, explicit validity checking, Transformer-based property prediction, structured design memory, and multi-island exploration. Through iterative generate--validate--evaluate--remember cycles, the agent uses feedback from both successful and failed candidates to guide chemically constrained search across linker, metal, and topology choices. We evaluate LEMO Agent on CH$_4$/N$_2$ and CO$_2$/N$_2$ separation tasks. 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