Multimodal Large Language Models (MLLMs) face critical privacy challenges due to the indiscriminate memorization of sensitive data. Existing unlearning methods, largely adapted from Euclidean paradigms, suffer from a geometric mismatch: they fail to disentangle specific instances from general concepts, causing catastrophic forgetting or unsafe substitution. We introduce LOTUS (Lorentz Transport for Unlearning Strategies), a framework for surgical semantic pruning within the Lorentz manifold. Leveraging hyperbolic geometry’s hierarchical nature, LOTUS employs an Inverted Entailment Cone Loss to sever the inheritance of sensitive concepts and a Lorentz Transport mechanism to align pruned features within the tangent space, ensuring compatibility with Euclidean backbones via a safety refusal prior. Experiments on MLLMU-Bench with LLaVA and Qwen show that LOTUS significantly outperforms baselines, effectively erasing targeted visual data while preserving general utility.