Creating a domain model, even for classical, domainindependent planning, is a notoriously hard knowledgeengineering task. A natural approach to solve this problem is to learn a domain model from observations. However, model learning approaches frequently do not provide safety guarantees: the learned model may assume actions are applicable when they are not, and may incorrectly capture actions' effects. This may result in generating plans that will fail when executed. In some domains such failures are not acceptable, due to the cost of failure or inability to replan online after failure. In such settings, all learning must be done offline, based on some observations collected, e.g., by some other agents or a human. Through this learning, the task is to generate a plan that is guaranteed to be successful. This is called the modelfree planning problem. Prior work proposed an algorithm for solving the model-free planning problem in classical planning. However, they were limited to learning grounded domains, and thus they could not scale. We generalize this prior work and propose the first safe model-free planning algorithm for lifted domains. We prove the correctness of our approach, and provide a statistical analysis showing that the number of trajectories needed to solve future problems with high probability is linear in the potential size of the domain model. We also present experiments on twelve IPC domains showing that our approach is able to learn the real action model in all cases with at most two trajectories. * This Arxiv paper is an extended version of a paper with the same title that have been accepted to the International Conference on Principles of Knowledge Representation and Reasoning (KR), 2021.