Complex manipulation tasks often require robots with complementary capabilities to collaborate. We introduce a benchmark for LanguagE-Conditioned Multi-robot MAnipulation (LEMMA) focused on task allocation and long-horizon object manipulation based on human language instructions in a tabletop setting. LEMMA features 8 types of procedurally generated tasks with varying degree of complexity, some of which require the robots to use tools and pass tools to each other. For each task, we provide 800 expert demonstrations and human instructions for training and evaluations. LEMMA poses greater challenges compared to existing benchmarks, as it requires the system to identify each manipulator's limitations and assign sub-tasks accordingly while also handling strong temporal dependencies in each task. To address these challenges, we propose a modular hierarchical planning approach as a baseline. Our results highlight the potential of LEMMA for developing future language-conditioned multi-robot systems.