Domain models enable autonomous agents to solve long-horizon tasks by producing interpretable plans. However, in open-world environments, a single general domain model cannot capture the variety of tasks, so agents must generate suitable task-specific models on the fly. Large Language Models (LLMs), with their implicit common knowledge, can generate such domains, but suffer from high error rates that limit their applicability. Hence, related work relies on extensive human feed-back or prior knowledge, which undermines autonomous, open-world deployment. In this work, we propose LODGE, a framework for autonomous domain learning from LLMs and environment grounding. LODGE builds on hierarchical abstractions and automated simulations to identify and correct inconsistencies between abstraction layers and between the model and environment. Our framework is task-agnostic, as it generates predicates, operators, and their preconditions and effects, while only assuming access to a simulator and a set of generic, executable low-level skills. Experiments on two International Planning Competition ( IPC) domains and a robotic assembly domain show that LODGE yields more accurate domain models and higher task success than existing methods, requiring remarkably few environment interactions and no human feedback or demonstrations.