LODGE studies domain models that help autonomous agents generate interpretable plans to solve long-term tasks. Because a single, general domain model cannot handle diverse tasks in an open environment, agents must generate task-specific models on the fly. While LLM can generate such domains, its high error rate limits its applicability. LODGE is a framework for LLM and environment-based unsupervised domain learning. It leverages hierarchical abstraction and automated simulation to identify and correct mismatches between abstraction layers and between models and environments. LODGE is task-agnostic and generates predicates, operators, preconditions, and effects based solely on access to a simulator and a set of general, executable, low-level techniques. Experimental results demonstrate that LODGE produces more accurate domain models and higher task success rates than existing methods, while requiring less environmental interaction and no human feedback or demonstration.