Open-world planning with incomplete knowledge is crucial for real-world embodied AI tasks. Despite that, existing LLM-based planners struggle with long chains of sequential reasoning, while symbolic planners face combinatorial explosion of states and actions for complex domains due to reliance on grounding. To address these deficiencies, we introduce LLM-Regress, an open-world planning approach integrating lifted regression with LLM-generated affordances. LLM-Regress generates sound and complete plans in a compact lifted form, avoiding exhaustive enumeration of irrelevant states and actions. Additionally, it makes efficient use of LLMs to infer goal-related objects and affordances without the need to predefine all possible objects and affordances. We conduct extensive experiments on three benchmarks and show that LLM-Regress significantly outperforms state-of-the-art LLM planners and a grounded planner using LLM-generated affordances.